A New Dynamic Model to Predict Transient and Steady State PV Temperatures Taking into Account the Environmental Conditions

Abstract

Photovoltaic (PV) cell and module temperature profiles, T c and T pv , respectively, developed under solar irradiance were predicted and measured both at transient and steady state conditions. The predicted and measured T c or T pv covered both a bare c-Si PV cell, by SOLARTEC, at laboratory conditions using a solar light simulator, as well as various c-Si and pc-Si modules (SM55, Bioenergy 195W, Energy Solutions 125W) operating in field conditions. The time constants, τ, of the T c and T pv profiles were determined by the proposed model and calculated using the experimentally obtained profiles for both the bare PV cell and PV modules. For model validation, the predicted steady state and transient temperature profiles were compared with experimental ones and also with those generated from other models. The effect of the ambient temperature, T a , wind speed, v w , and the solar irradiance, I T , on the model performance, as well as of the mounting geometries, was investigated and incorporated in the prediction model. The predicted temperatures had the best matching to the measured ones in comparison to those from six other models. The model developed is applicable to any geographical site and environmental conditions. Energies 2019, 12, 2 2 of 17 b.Theoretical based semi-empirical models, a mixture of Physics based processes elaborated on implicit functions, which through regression analysis incorporate the environmental conditions and develop expressions to predict T pv including geometrical factors like PV module inclination, sun-tracking systems, BIPV [6,8,21]. c.Approaches based on Artificial Neural Networks (ANN) [5,10,22].An assessment of the T pv prediction models discloses that those which have incorporated the radiation exchanges and the air flow regimes, where heat extraction off the modules is affected specifically, provide values closer to the measured ones [6,7,[23][24][25]. A comparison among the models is necessary as to conclude on the conditions T pv is predicted effectively and consistently. It is, therefore, necessary to compare T pv models extensively to examine their validity in any PV configuration as the ones studied in [20,[26][27][28][29].A time dependent temperature profile is developed in a PV cell when under solar irradiance, I T , [8,30]. The latter is the main factor contributing to the development of the temperature profile in which the ambient temperature T a and the wind speed play a role too. This profile has a straight relationship with I T at low Concentration Ratio, C, conditions, with C < 4, where C = I T /10 3 W/m 2 , and a strong dependence on the wind speed, v w ; that is, T c (t; I T , v w ). T c (t) depends, also, on the cell structure and the material composition of its layers. Figure 1 shows a section of a PV cell with its characteristic layers which govern the heat conduction causing an effect on the time constant, τ, of the temperature profiles. T c (t) or T pv (t), either the PV module is heated or cooled due to changes in the environmental conditions, is described ...

Dynamic Electro-Thermal PV Temperature and Power Output Prediction Model for Any PV Geometries in Free-Standing and BIPV Systems Operating under Any Environmental Conditions

“…The predicted T PVb profile responding to the irradiance drop also follows an exponential decay whose analysis gives a time constant equal to 5.5 min. This is in agreement with the theoretically derived τ = 1/F 2 and slightly higher than the time constant 4.5 min reported in [23] for free-standing PV, as expected, since τ increases with (mc p ) total and decreases with U. Figure 3, including also a comparison with the predicted temperature profiles as generated by using 3 other models.…”

“…This is clearly shown in the drop in measured irradiance on the PV plane in Figure 4. At that time, the measured PV temperature experienced an exponential decay which is explained through Equation (23). The predicted T PVb profile responding to the irradiance drop also follows an exponential decay whose analysis gives a time constant equal to 5.5 min.…”

“…The mass heat capacity (mc p ) for the various layers of the module is expressed in the above equations normalised to the unit surface, with value for the front glass 4500 JK −1 m −2 , the EVA 502 JK −1 m −2 , the c-Si solar cell 355 JK −1 m −2 , and the Tedlar 150 JK −1 m −2 , [23]. (mc p ) total = Σ(mc p ) i, where i refers to each of the above layers.…”

“…(mc p ) total = Σ(mc p ) i, where i refers to each of the above layers. The material properties and geometry of the different layers are provided in [23].…”

“…In another equivalent approach to the iterative algorithmic process presented above, the PV temperature at the back of the module may be predicted from the following set of equations derived from transient EBEs, as derived by the authors in [23]. This requires only a couple of iterations to update the value of the T pv dependent parameters: η c , and the heat losses' coefficients, approximating T PVf to T PVb in the determination of heat losses' coefficients.…”