A simple non-linear model for the effect of partial shade on PV systems

Abstract

The effect of shade from one PV module on another is incorporated into a model for the power generated by PV systems. The model is calibrated with data from the Tucson Electric Power solar test yard. Shade de-rating factors from the model are compared with data every minute of the day and every day of the year. The model is then used to predict final yields (kWh/kWoc) for different PV system deployments with various (non-tracking) module orientations and ground-cover ratios. Several heuristics are put forth to help understand how the observed non-linear response to shade can impact the yield from PV systems. In one example, we find that a PV system deployed in the Tucson Electric Power solar test yard could produce 22% more kWh for the month of December (and 3.8% more annually) if the modules were separated by twice as much distance. In another example, we predict that a system in Tucson with south-facing modules at 12-degrees from horizontal can generate 1.5 times as many kWhlyr per square-meter of land compared to a system with modules at 32-degrees (the latitude angle).These examples emphasize the non-linear impact of partial shade on PV system performance.

Partial Shading Analysis of Multistring PV Arrays and Derivation of Simplified MPP Expressions

“…So far, expressions (14), (17), (18) and (19) provide the voltage and current of all MPPs of a partially shaded PV array, considering the multiple irradiance levels G i j on different parts of the array. To take into account the temperature effect, the following expressions can be used for the terms I mp , V mp and V oc :…”

“…Concerning multi-string arrays, in [17] and [18], simple, non-electrical models are proposed, which are empirical in nature and are mainly based on a simplified consideration of the shading phenomenon, demonstrating only moderate accuracy. In [19] more accurate expressions are developed, yet limited to one level of shade.…”

Shading on Photovoltaic Collectors on Rooftops

“…Shading causes uneven distribution of the incident solar radiation on the PV modules, resulting in the formation of steps across the I-V characteristics. Articles that include analytical expressions for shading on PV collectors in solar fields are mentioned in [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19]. Shadow analysis and its effect on solar PV systems for flat-plate collectors was started early by [3] and followed by [6][7][8].…”

Modification and upgrade of AzRISE/TEP solar photovoltaic test yard

“…The site has served as an enabling test location in support of TEP's solar energy generation implementation plan as well as for characterization and evaluation projects involving solar energy manufacturers and academic researchers [1][2][3] . Outdoor testing facilities such as this are essential to understanding the anticipated performance of photovoltaic modules under field-consistent environments [3][4][5][6][7] that extend beyond those used in standard test conditions (STC); the latter do not take into account location-dependent temperature and humidity climates, shading, atmospheric conditions, or soiling. Moreover, the data from the test yard can provide additional insight into the validity of laboratory-based performance measurements [8] .…”