This document summarizes the equations and applications associated with the photovoltaic array performance model developed at Sandia National Laboratories over the last twelve years. Electrical, thermal, and optical characteristics for photovoltaic modules are included in the model, and the model is designed to use hourly solar resource and meteorological data. The versatility and accuracy of the model has been validated for flat-plate modules (all technologies) and for concentrator modules, as well as for large arrays of modules. Applications include system design and sizing, 'translation' of field performance measurements to standard reporting conditions, system performance optimization, and real-time comparison of measured versus expected system performance. 3 ACKNOWLEDGEMENTS

The term "temperature coefficient" has been applied to several different photovoltaic performance parameters, including voltage, current, and power. The procedures for measuring the coefficient(s) for modules and arrays are not yet standardized, and systematic influences are common in the test methods used to measure them. There are also misconceptions regarding their application. Yet, temperature coefficients, however obtained, play an important role in PV system design and sizing, where often the worst case operating condition dictates the array size.This paper describes effective methods for determining temperature coefficients for cells, modules, and arrays; identifies sources of systematic errors in measurements; gives typical measured values for modules; and provides guidance for their application in system engineering.

Our investigations of both new and field-aged photovoltaic modules have indicated that, in general, today's commercially available modules are a highly reliable product. However, by using new test procedures, subtle failure mechanisms have also been identified that must be addressed in order to achieve 30-year module lifetimes. This paper summarizes diagnostic test procedures, results, and implications of in-depth investigations of the performance and durability characteristics of commercial modules after long-term field exposure. A collaborative effort with U.S. module manufacturers aimed at achieving 30-year module lifetimes is also described. Sandia is a multi-program laboratory operated by Sandia Corporation, a Lockheed Martin Company, for the U.S. Department of Energy under contract DE-ACO4-94AL8500.

SOLAR SPECTRAL INFLUENCEHistorically, two time-of-day dependent factors have complicated the characterization of photovoltaic module and array performance; namely, changes in the solar spectrum over the day and optical effects in the module that vary with the solar angle-of-incidence. This paper describes straightforward methods for directly measuring the effects of these two factors. Measured results for commercial modules, as well as for typical solar irradiance sensors (pyranometers) are provided. The empirical relationships obtained from the measurements can be used to improve the methods used for system design, verification of performance after installation, and diagnostic monitoring of performance during operation.

The most relevant basis for designing photovoltaic systems is their annual energy production, which is also the best metric for monitoring their long-term performance. An accurate array performance model based on established testing procedures is required to confidently predict energy available from the array. This model, coupled with the performance characteristics of other baiance-of-system components, provides the tool necessary to calculate expected system performance and to compare actual versus expected energy production. Using such a tool, this paper quantifies the affect of the primary factors influencing the dwnergy available from different photovoltaic module technologies. and contrasts these influences with other system-level factors that oflen result in significanUy less acenergy delivered to the load than the array is capable of providing. Annual as well as seasonal energy production is discussed in the context of both grid-tied and stand-alone photovoltaic systems.