There are several models aimed at the prediction of the photovoltaic potential. Klise and Stein [153] provide an extensive review of the most common PV assessment methods. As a subsequent work, the Sandia National Laboratories worked on a set of collaborative open-source libraries providing access to three of these models, namely the PVwatts model [73], the Sandia Array Performance Model [150] and
Chapter 2. Multidisciplinary research background
the Single Diode Model [66].
These PV assessment methods are composed of multiple physical models. We list here below the main models, describing their fundamental parameters and highlighting the aspects of complexity.
2.2.6.1 Plane of Array Irradiance
In spite of PV technologies having different spectral responses, standard PV prediction models do not include such information. Similarly, they do not make difference between the components of solar radiation, which have typically very different spectra. For solar energy applications, the target solar radiation quantity is therefore the global irradiance incident on the Plane of Array (POA), also called Global Tilted Irradiance (GTI). The POA irradiance is usually modeled based on the main components of solar radiation at the horizontal surface (GHI, DHI) and normal to the sun (DNI) [271].
The calculation of the direct incident solar radiation is straightforward, once the angle of incidence of the DNI on the tilted plane is known [271]. For most applications, the calculation of reflected solar radiation can be neglected (as its contribution for installation tilts is low below 45°tilts) or calculated with a number of assumptions, such as infinite, horizontal and isotropically-reflective foreground [271]. The sky diffuse solar irradiance is the most complex component to calculate. This component is crucial in overcast sky conditions, in which it constitutes the 100% of the GHI, while giving a relatively small contribution during clear or partly-cloudy conditions (<30% of GHI) [271]. Different models are available and a complete review was conducted by Yang [321], while the most popular are the ones developed by Perez et al. [215], which generally perform well with hourly data [271].
2.2.6.2 Cell and module temperature
As seen in Section 2.2.4.1, the cell temperature is affecting the performance of many technologies of solar cells, in particular the crystalline silicon ones. Typically, the cell temperature is higher than the air temperature, because of the absorptivity of building materials. The type of installation also affects the ventilation. In this sense, BIPV modules are generally more subject to overheating because they are less ventilated than an open-rack system, through which the wind can freely flow.
The Sandia Array Performance Model [149] is a popular module for predicting the cell and module temperature. It differentiates between the module (back surface) Tmand cell temperature Tc. These
are calculated with two different empirical equations: Tm= E ·
ea+b·W S+ Ta (2.1)
where Tmis the back surface air temperature (°C), Tais the ambient air temperature (°C), E is the
solar irradiance incident on module surface (W/m2), WS is the wind speed measured at standard 10-m height (m/s) Tc= Tm+ E Eo· ΔT (2.2) 18
2.2. Photovoltaic systems
Table 2.4 – PVWatts’s temperature coefficients for different module types.
Source Dobos [73, p. 4]
Module type Cover type Temperature coefficient (γ)
Standard Glass -0.47%/°C
Premium Anti-reflective -0.35%/°C
Thin film Glass -0.20 %/°C
2.2.6.3 Module performance
The simplest module performance often used as a rule of thumb for energy production is the following:
E= IPOA· η · A (2.3)
where IPOAis the irradiance on the Plane of Array and A andη are respectively the Area and the
efficiency of the module. This model does not consider the effect of boundary conditions presented in Section 2.2.4. Moreover, the accuracy of this model is largely dependent on the conditions at which the efficiencyη has been measured. Many manufacturers provide only efficiency at STC1, which is usually larger than the efficiency at the actual test conditions (especially in hot climates), giving thus an overestimation of the energy production E . Some manufactures provide the PTC efficiency2, which is closer to real world conditions.
It is also possible to have a more accurate estimate of the efficiencyη at the actual cell temperature by using a temperature coefficientγ. For example, PVWatts use the coefficients listed in Table 2.4. Some manufactures include the Temperature at NOCT3and the relative temperature coefficientγ from which it is possible to estimate the efficiency:
η = ηSTC· [1 + γ(Tcell− TSTC)] (2.4)
Some computer software integrate more complex models for module performance. [153] provides a re- view of 23 PV performance models, among which we find PVWatts, the 5-parameter Array Performance Model [66]. These models are included in the popular software System Advisor Model (SAM), which aims at providing an assessment of PV as a system, including then also the financial part. They are also included in PVLib, a Python library for photovoltaic prediction [112], based on an original MATLAB version [286]. Because of their implementation in open-source libraries which make these models particularly suitable for this thesis application, we will briefly list their main characteristics:
• PVWatts is an on-line calculation tool developed by the National Renewable Energy Laboratory principally intended for rapid assessment of PV energy generation. PVWatts is a popular model for early-design estimations, as it requires few input, while providing validated results [73]. It was conceived for use in the homonym web tool by NREL4, but it is also available as calculation model in SAM and PVLIB. The web application has been online since 1999 and is currently at
1Standard Test Conditions, i.e. cell temperature of 25°C, irradiance of 1000 W/m2and an air mass 1.5 (1.5 AM) spectrum 2PVUSA Test Conditions, i.e. air temperature of 20°C at 10 m above ground level, irradiance of 1000 W/m2, 1.5 m/s wind
speed and an air mass 1.5 (1.5 AM) spectrum
3Nominal Operating Cell Temperature conditions, i.e. air temperature of 20°C, irradiance of 800 W/m2, 1 m/s wind speed
and mounting with open back side [114, 12]
Chapter 2. Multidisciplinary research background
version 4 [73]. Unlike other models, it does not require a particular PV product as input, but it is rather intended for a family of products (e.g. “standard”, “premium” or “thin film” module types). For this reason, in additional to the prediction models, it contains also many default values. • The Sandia Array Performance Model (SAPM) is an advanced performance model for estimating
the DC current of an array. It can be coupled with the the Sandia Inverter Performance Model to provide the conversion from DC to AC current. It is based on a series of empirical measurements of commercial PV modules, which are listed in a database. This database is maintained and regularly updated by Sandia. At the time of writing, this list included 523 modules.
• The 5-parameter model, or De Soto model, is a semi-empiric model which express the five parameters of the single-diode models as a function of cell temperature and POA irradiance. The IV-curve of a PV cell (but also of a module or an array) can be in fact described with ideal circuit models including a single diode under constant temperature and POA irradiance. All single-diode models are governed by five main parameters: light current, diode reverse saturation current, series resistance, shunt resistance, and ideality factor. The parameters for the De Soto model, i.e., short circuit current, open circuit voltage, voltage at maximum power point, current at maximum power point and the temperatures coefficients at both open circuit voltage and short circuit current, are usually provided by manufacturers in the technical data-sheet of the product or can be obtained many products through the California Energy Commission (CEC) database, already described in Section 2.2.2. This list is 40 times larger than the Sandia Modules database needed to run the SAPM model. The main advantage of using this model is therefore the applicability for a large number of market products.The 5-parameter model in its current version is based on the work by De Soto et al. [66], but its origin dates back to 1989 and is constantly evolving in its version maintained by the University of Wisconsin5This model is better suited for crystalline silicon modules, while it works also for thin-film technologies [153].
An experimental study conducted by Cameron et al. [41], compared these models as well as three other ones (a simple fixed efficiency model, an efficiency model with temperature coefficient correction, and PVmode, an early model developed by Sandia) on the performance of PV arrays of different size (1.1, 1.11 and 2.3 kW). The study shows that all models have generally error lower than 10%. The SAPM model has the best accuracy, while PVWatts and the 5-parameter model have similar results, with the latter improving for larger arrays.
2.2.6.4 System and inverter performance
The system performance includes modeling losses due to different factors. Dobos [73] cites the following real-world system losses reducing the DC current: soiling, shading, snow, mismatch, wiring, connections, light-induced degradation, nameplate rating, system age, and operational availability. In the PVWatts model, the total system losses accounts for 14% of the DC energy [73].
In addition to these losses, the transformation from DC to AC energy needs an inverter performance to be modeled. Similarly than for module efficiency, typical data sheets provide only the maximum efficiency, while the inverter efficiency is a function of input power level and input voltage [41]. However, it should be considered that modeling the system and inverter performance, requires many hypothesis concerning the arrangement of the modules and the strings, so as to minimize the number
5http://sel.me.wisc.edu/software.shtml, last accessed on March 28, 2018.
2.2. Photovoltaic systems
of inverters while not undermining the performance due to partial shading. This problem has been treated by previous studies using optimization algorithms [89]. For the scope of our work, which focuses on comparisons rather than on absolute values, we argue that the DC yield is a good proxy of the solar potential. The AC performance will be confronted to a real system in Chapter 13 using a fixed Performance Ratio.