Publications

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The PV lifetime project must select a sample size (number of PV modules) for each PV system to be deployed. In this memorandum, we show how the uncertainty in measured degradation depends on the selected sample size.

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We describe and compare two methods for modeling irradiance on the back surface of rack-mounted bifacial PV modules: view factor models and ray-tracing simulations. For each method we formulate one or more models and compare each model with irradiance measurements and short circuit current for a bifacial module mounted a fixed tilt rack with three other similarly sized modules. Our analysis illustrates the computational requirements of the different methods and provides insight into their practical applications. We find a level of consistency among the models which indicates that consistent models may be obtained by parameter calibrations.

Short circuit current (Isc) depends on the effective irradiance incident upon a PV module. Effective irradiance is highly correlated with broadband irradiance, but can vary slightly as the spectral content of the incident light changes. We explore using a few spectral wavelengths with broadband irradiance to predict Isc for ten modules of varying technologies (silicon, CIGS, CdTe). The goal is to identify a few spectral wavelengths that could be easily (and economically) measured to improve PV performance modeling.

The Sandia Array Performance Model (SAPM), a semi-empirical model for predicting PV system power, has been in use for more than a decade. While several studies have presented laboratory intercomparisons of measurements and analysis, detailed procedures for determining model coefficients have never been published. Independent test laboratories must develop in-house procedures to determine SAPM coefficients, which contributes to uncertainty in the resulting models. In response to requests from commercial laboratories and module manufacturers, Sandia has formally documented the measurement and analysis methods as a supplement to the original model description. In this paper we present a description of the measurement procedures and an example analysis for calibrating the SAPM.

Commonly used performance models, such as PVsyst, Sandia Array Performance Model (SAPM), and PV LIB, treat the PV array as being constructed of identical modules. Each of the models attempts to account for mismatch losses by applying a simple percent reduction factor to the overall estimated power. The present work attempted to reduce uncertainty of mismatch losses by determining a representative set of performance coefficients for the SAPM that were developed from a characterization of a sample of modules. This approach was compared with current practice, where only a single module’s thermal and electrical properties are testing. However, the results indicate that minimal to no improvements in model predictions were achieved.

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We describe the method used to simulate one year of AC power at one-minute intervals for a large collection of hypothetical utility-scale photovoltaic plants of varying size, employing either fixed-tilt PV modules or single-axis tracking, and for distribution-connected photovoltaic (DPV) power systems assumed for a number of metropolitan areas. We also describe the simulation of an accompanying day-ahead forecast of hourly AC power for utility-scale plants and DPV systems such that forecast errors are consistent with errors reported for current forecasting methods. The results of these simulations are intended for use in a study that examines the possible effects of increased levels of photovoltaic (PV) generation bulk on power variability within the Tennessee Valley Authority (TVA) and Southern Company service territories.

The Sandia Array Performance Model (SAPM), a semi-empirical model for predicting PV system power, has been in use for more than a decade. While several studies have presented comparisons of measurements and analysis results among laboratories, detailed procedures for determining model coefficients have not yet been published. Independent test laboratories must develop in-house procedures to determine SAPM coefficients, which contributes to uncertainty in the resulting models. Here we present a standard procedure for calibrating the SAPM using outdoor electrical and meteorological measurements. Analysis procedures are illustrated with data measured outdoors for a 36-cell silicon photovoltaic module.

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We present a simple algorithm for identifying periods of time with broadband global horizontal irradiance (GHI) similar to that occurring during clear sky conditions from a time series of GHI measurements. Other available methods to identify these periods do so by identifying periods with clear sky conditions using additional measurements, such as direct or diffuse irradiance. Our algorithm compares characteristics of the time series of measured GHI with the output of a clear sky model without requiring additional measurements. We validate our algorithm using data from several locations by comparing our results with those obtained from a clear sky detection algorithm, and with satellite and ground-based sky imagery.

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Air mass modifiers are frequently used to represent the effects of solar spectrum on PV module current. Existing PV module performance models assume a single empirical expression, a polynomial in air mass, for all locations and times. In this paper, air mass modifiers are estimated for several modules of different types from IV curves measured with the modules at fixed orientation in three climatically different locations around the United States. Systematic variation is found in the effect of solar spectrum on PV module current that is not well approximated by the standard air mass modifier polynomial.

The SunShot Initiative coordinates research, development, demonstration, and deployment activities aimed at dramatically reducing the total installed cost of solar power. The SunShot Initiative focuses on removing critical technical and non-technical barriers to installing and integrating solar energy into the electricity grid. Uncertainty in projected power and energy production from solar power systems contributes to these barriers by increasing financial risks to photovoltaic (PV) deployment and by exacerbating the technical challenges to integration of solar power on the electricity grid.

PV performance models are used to quantify the value of PV plants in a given location. They combine the performance characteristics of the system, the measured or predicted irradiance and weather at a site, and the system configuration and design into a prediction of the amount of energy that will be produced by a PV system. These predictions must be as accurate as possible in order for finance charges to be minimized. Higher accuracy equals lower project risk. The Increasing Prediction Accuracy project at Sandia focuses on quantifying and reducing uncertainties in PV system performance models.

The Advanced Measurement and Analysis of PV Derate Factors project focuses on improving the accuracy and reducing the uncertainty of PV performance model predictions by addressing a common element of all PV performance models referred to as “derates”. Widespread use of “rules of thumb”, combined with significant uncertainty regarding appropriate values for these factors contribute to uncertainty in projected energy production.

The Characterizing Emerging Technologies project focuses on developing, improving and validating characterization methods for PV modules, inverters and embedded power electronics. Characterization methods and associated analysis techniques are at the heart of technology assessments and accurate component and system modeling. Outputs of the project include measurement and analysis procedures that industry can use to accurately model performance of PV system components, in order to better distinguish and understand the performance differences between competing products (module and inverters) and new component designs and technologies (e.g., new PV cell designs, inverter topologies, etc.).

We present an algorithm to determine parameters for the photovoltaic module perf ormance model encoded in the software package PVsyst(TM) version 6. Our method operates on current - voltage (I - V) measured over a range of irradiance and temperature conditions. We describe the method and illustrate its steps using data for a 36 cell crystalli ne silicon module. We qualitatively compare our method with one other technique for estimating parameters for the PVsyst(TM) version 6 model .

We report an analysis that compares global horizontal irradiance (GHI) estimates from version 3 of the National Solar Radiation Database (NSRDB v3) with surface measurements of GHI at a wide variety of locations over the period spanning from 2005 to 2012. The NSRDB v3 estimate of GHI are derived from the Physical Solar Model (PSM) which employs physics-based models to estimate GHI from measurements of reflected visible and infrared irradiance collected by Geostationary Operational Environment Satellites (GOES) and several other data sources. Because the ground measurements themselves are uncertain our analysis does not establish the absolute accuracy for PSM GHI. However by examining the comparison for trends and for consistency across a large number of sites, we may establish a level of confidence in PSM GHI and identify conditions which indicate opportunities to improve PSM. We focus our evaluation on annual and monthly insolation because these quantities directly relate to prediction of energy production from solar power systems. We find that generally, PSM GHI exhibits a bias towards overestimating insolation, on the order of 5% when all sky conditions are considered, and somewhat less (-3%) when only clear sky conditions are considered. The biases persist across multiple years and are evident at many locations. In our opinion the bias originates with PSM and we view as less credible that the bias stems from calibration drift or soiling of ground instruments. We observe that PSM GHI may significantly underestimate monthly insolation in locations subject to broad snow cover. We found examples of days where PSM GHI apparently misidentified snow cover as clouds, resulting in significant underestimates of GHI during these days and hence leading to substantial understatement of monthly insolation. Analysis of PSM GHI in adjacent pixels shows that the level of agreement between PSM GHI and ground data can vary substantially over distances on the order of 2 km. We conclude that the variance most likely originates from dramatic contrasts in the ground's appearance over these distances.

We report an uncertainty and sensitivity analysis for modeling AC energy from ph otovoltaic systems . Output from a PV system is predicted by a sequence of models. We quantify u ncertainty i n the output of each model using empirical distribution s of each model's residuals. We propagate uncertainty through the sequence of models by sampli ng these distributions to obtain a n empirical distribution of a PV system's output. We consider models that: (1) translate measured global horizontal, direct and global diffuse irradiance to plane - of - array irradiance; (2) estimate effective irradiance; (3) predict cell temperature; (4) estimate DC voltage, current and power ; (5) reduce DC power for losses due to inefficient maximum power point tracking or mismatch among modules; and (6) convert DC to AC power . O ur analysis consider s a notional PV system com prising an array of FirstSolar FS - 387 modules and a 250 kW AC inverter ; we use measured irradiance and weather at Albuquerque, NM. We found the uncertainty in PV syste m output to be relatively small, on the order of 1% for daily energy. We found that unce rtainty in the models for POA irradiance and effective irradiance to be the dominant contributors to uncertainty in predicted daily energy. Our analysis indicates that efforts to reduce the uncertainty in PV system output predictions may yield the greatest improvements by focusing on the POA and effective irradiance models.

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We report an evaluation of the accuracy of combinations of models that estimate plane-of-array (POA) irradiance from measured global horizontal irradiance (GHI). This estimation involves two steps: 1) decomposition of GHI into direct and diffuse horizontal components and 2) transposition of direct and diffuse horizontal irradiance (DHI) to POA irradiance. Measured GHI and coincident measured POA irradiance from a variety of climates within the United States were used to evaluate combinations of decomposition and transposition models. A few locations also had DHI measurements, allowing for decoupled analysis of either the decomposition or the transposition models alone. Results suggest that decomposition models had mean bias differences (modeled versus measured) that vary with climate. Transposition model mean bias differences depended more on the model than the location. When only GHI measurements were available and combinations of decomposition and transposition models were considered, the smallest mean bias differences were typically found for combinations which included the Hay/Davies transposition model.

Many popular models for photovoltaic system performance employ a single diode model to compute the I - V curve for a module or string of modules at given irradiance and temperature conditions. A single diode model requires a number of parameters to be estimated from measured I - V curves. Many available parameter estimation methods use only short circuit, o pen circuit and maximum power points for a single I - V curve at standard test conditions together with temperature coefficients determined separately for individual cells. In contrast, module testing frequently records I - V curves over a wide range of irradi ance and temperature conditions which, when available , should also be used to parameterize the performance model. We present a parameter estimation method that makes use of a fu ll range of available I - V curves. We verify the accuracy of the method by recov ering known parameter values from simulated I - V curves . We validate the method by estimating model parameters for a module using outdoor test data and predicting the outdoor performance of the module.

We present an algorithm to calculate the azimuth and elevation angles for a dual axis tracker to be pointed away from the sun with a desired orientation between the sun and the tracker face. Desired tracker positions are specified in terms of angle of incidence (AOI) and AOI direction, i.e., the direction of the projection of the sun beam onto the plane of the tracker face. This algorithm was developed to enable characterization of the electro-optical response of photovoltaic (PV) and concentrating PV (CPV) modules with anisotropic response to AOI.

In order to reliably simulate the energy yield of photovoltaic (PV) systems, it is necessary to have an accurate model of how the PV modules perform with respect to irradiance and cell temperature. Building on a previous study that addresses the irradiance dependence, two approaches to fit the temperature dependence of module power in PVsyst have been developed and are applied here to recent multi-irradiance and temperature data for a standard Yingli Solar PV module type. The results demonstrate that it is possible to match the measured irradiance and temperature dependence of PV modules in PVsyst. Improvements in energy yield prediction using the optimized models relative to the PVsyst standard model are considered significant for decisions about project financing.

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We present a method for measuring the series resistance of the PV module, string, or array that does not require measuring a full IV curve or meteorological data. Our method relies only on measurements of open circuit voltage and maximum power voltage and current, which can be readily obtained using standard PV monitoring equipment; measured short circuit current is not required. We validate the technique by adding fixed resistors to a PV circuit and demonstrating that the method can predict the added resistance. Relative prediction accuracy appears highest for smaller changes in resistance, with a systematic underestimation at larger resistances. Series resistance is shown to vary with irradiance levels with random errors below 1.5% standard deviation.

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