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Page • Introduction Started in 2016, the PV Lifetime Project is measuring PV module and system degradation profiles over time with the aim of distinguishing different module types and technology. Outdoor energy monitoring in different climates will be supplemented with regular testing under repeatable test conditions indoors. The focus will be on...

Page • PV performance metrics are quantities that are used to evaluate and compare the performance between systems and between different sites and climates.  A 2014 report by SunSpec Alliance and San Jose University entitled: PV System Performance Assessment, provides a good technical summary of a collection of PV performance metrics in use...

Page • This part of the PVPMC website is meant to highlight current research projects being performed by the PVPMC community.  It offers members of the PVPMC an opportunity to share technical goals, approaches, and results of their research. Project Areas Bifacial PV Project (2016-2018) – Joint project with Sandia National Laboratories, National...

Page • Matthew Lave, Robert J. Broderick, Matthew J. Reno, Solar variability zones: Satellite-derived zones that represent high-frequency ground variability, Solar Energy, Volume 151, 15 July 2017, Pages 119-128, ISSN 0038-092X. Abstract: To determine the impact of solar variability to electric grid operations, appropriate samples of solar variability must be used, but determining appropriate variability...

Page • The PV_LIB Toolbox provides a set of well-documented functions for simulating the performance of photovoltaic energy systems. Currently there are two distinct versions (pvlib-python and PVILB for Matlab) that differ in both structure and content.   Both versions were initially developed at Sandia National Laboratories but have since been offered...

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Page • About the Modeling Collaborative Sandia National Laboratories is facilitating a collaborative group of photovoltaic (PV) professionals (PV Performance Modeling Collaborative or PVPMC).  This group is interested in improving the accuracy and technical rigor of PV performance models and analyses.  Such models are used to evaluate current performance (performance index) and...

Page • The PV performance modeling application, PVsyst, implements the following cell temperature model: $$T_{c}= T_{a}+E_{POA}\frac{\alpha \left (1-eta_{m} \right)}{U_{0}+U_{1}\times WS}$$ where $$T_{c}$$ is cell temperature (°C)$$T_{a}$$ is ambient air temperature (°C)$$\alpha$$ is the absorption coefficient of the module (PVsyst default value is 0.9)$$E_{POA}$$ is the irradiance incident on the plane of the module or array ($$W/m^{2}$$)$$eta_{m}$$ is the...

Page • PVsyst is a software package for modeling complete photovoltaic systems including PV modules, inverters, energy storage, and electrical connection components. PVsyst employs a single diode module model with the following ancillary equations. Note that here we use $$I_L$$ and $$\alpha_{lsc}$$ to denote the light current, absorbed irradiance and temperature coefficient of $$_{sc}$$, respectively, whereas in the PVsyst User’s Guide, $$I_{PH}$$, $$G$$, and $$\mu_{lsc}$$ are used for...

Page • The PVWatts model is provided by the National Renewable Energy Laboratory (NREL) as an online PV performance modeling application.  The equations that underlie PVWatts are really quite simple.  There are two primary input variables: Effective irradiance ($$E_e$$)PV cell temperature ($$T_c$$) PVWatts relates these two variables to the maximum power point...

Page • Ray Tracing Work at NREL RADIANCE is a reverse ray tracing model typically used for lighting design of buildings. This simulation tool provides physically realistic image rendering and illuminance mapping, and has been used previously for the modeling of bifacial PV installations [Lo, Lim and Rahman, 2015]. We have conducted initial...

Page • Ray tracing models follow light from the source to the surface of interest (forward ray tracing) or from the surface of interest back to the source (reverse ray tracing). These models are typically based on a Monte Carlo approach that simulates hundreds or thousands of different rays and uses optical...

Page • The Reindl sky diffuse irradiance model (Reindl et al., 1990;Reindl et al., 1990b; Loutzenhiser et al., 2007 ) represents three components of diffuse radiation on the POA, including isotropic, circumsolar brightening, and horizon brightening.  This model extends the Hay and Davies model by adding an additional factor to the “brightening” term to...

Page • The Sandia cell temperature model estimates cell temperature from module temperature, $$T_m$$, plane of array irradiance, $$E_{POA}$$, and a temperature difference parameter, $$\Delta T$$. This difference parameter defines the temperature difference between the module and cell temperature. The model form is: $$T_c=T_m +\frac{E_{POA}}{E_0}\Delta T$$, where $$E_{0}$$ is a reference irradiance (1000 W/$$m^{2}$$). Content contributed by Sandia National...

Page • Sandia has suggested using a 5th order polynomial function to represent angular optical losses on short circuit current (Isc) [1]. $$f2\left( \theta_{AOI} \right) = b_0 + b_1\theta_{AOI} + b_2\theta_{AOI}^2 + b_3\theta_{AOI}^3 +b_4\theta_{AOI}^4+b_5\theta_{AOI^5}$$ where the coefficient vector, $$b$$, is determined from fitting experimental data measured outdoors. An example result of this model...

Page • The Sandia Inverter Model provides a means to predict AC output power ($$P_{AC}$$) from DC input power ($$P{_{DC}}$$). The form of the model is as follows: $$P_{AC}=\left \{ \frac{P_{AC0}}{A-B} -C\left ( A-B \right )\right \}\left ( P_{DC}-B \right )+C\left ( P_{DC}-B \right )^{2}$$ where $$A=P_{DC0}\left \{ 1+C_{1}\left ( V_{DC}-V_{DC0} \right )...

Page • Sandia proposes the following model to estimate module temperature, : $$T_{m} = E_{POA}\cdot (e^{a+b\cdot WS} ) + T_a$$ $$E_{POA}$$ = Solar irradiance incident on the module (POA) (W/m^2)$$T_a$$ = Ambient air temperature (°C)$$WS$$ = Wind speed (m/s) a and b are parameters that depend on the module construction and materials as well as on the mounting configuration...

Page • The Sandia PV Array Performance Model (SAPM) defines five points on the IV curve.  These points are shown in the figure below. The SAPM defines the primary points ($$I_{sc}$$, $$I_{mp}$$, $$V_{oc}$$, and $$V_{mp}$$) with the following equations: $$I_{sc}=I_{sc0}\times f_{1} \left ( \frac{E_{b}f_{2}+f_{d}E_{d}}{E_{0}} \right )\times \left ( 1+\alpha _{Isc}\left ( T_{c}-T_{0} \right ) \right...

Page • Sandia has coded a view factor model that estimates back-side irradiance across a row of bifacial modules, accounting for the row’s shadow on the ground and assuming an isotropic model for sky diffuse irradiance. Figure 1 and Figure 2 show the modeled variation in back-side irradiance by cell at noon...

Page • Sandia National Laboratories has developed a function that approximates the position of the sun quite accurately.  This function, along with Matlab source code, is available as part of the PV_LIB Toolbox.  The function is pvl_ephemeris.  The calculation is based on an internal course, Engineering Astronomy, developed by Grover Hughes, and...

Page • Here, irradiance incident on the array (calculated in the previous step) is further reduced by shading, soiling, and reflection losses.  Various modeling approaches have been developed to account for these reductions.  They will be examined in detail in the following sections.

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