Clouds, aerosols, water vapor and other atmospheric constituents influence solar energy reaching the earth's surface. Each of these atmospheric constituents has it's own inherent scale of temporal and spatial variability and they in turn influence the variability in the amount of solar radiation reaching the earth's surface. This combined influence of the atmospheric constituents and their separate variability characteristics makes solar variability modeling a complicated task.

Output from photovoltaic (PV) power plants is dependent on the amount of solar energy reaching the surface. Therefore variability in solar radiation results in variability in PV plant output. The issue of variability in PV plant output has become important in the last couple of years as utility scale PV plants go online and increase in size. Understanding variability in PV plant output requires an understanding of (a) the spatial and temporal variability of solar radiation; (b) the influence of this solar variability on PV plant output.

The goal of this paper is to understand what temporal and spatial scales of variability in Global Horizontal Radiation (GHI) are important to a PV plants and what measurements are needed to be able to characterize them. As solar radiation measuring instruments are point receivers it is important to understand how those measurements translate to energy received over a larger spatial extent. Also of importance is the temporal natural of variability characterized not at a single point on the ground but over large spatial areas.  In this research we use high temporal and spatial resolution measurements from multiple (17) sensors at a 1 square km site in Hawaii to measure GHI. Using these measurements we create solar radiation fields (Figure 1) at various spatial and temporal scales using a wide range of interpolation techniques.

These solar fields are then used to create plant power output for various size PV plants.  As various interpolation schemes can produce different distributions we investigate the impact of interpolation schemes on GHI and power output distribution. While power output from PV plants is an important quantity the temporal variability of power is a matter of concern to utilities. In Figure 2 we compare the cumulative distribution of 60-second plant variability (defined as ramps) for a 30 MW plant for the various interpolation schemes. We use 1 month of solar radiation from July 2010 for this case.

While understanding the nature of solar spatial and temporal variability is our primary goal it is also important to understand if a PV plant occupying a certain area can be modeled using a smaller subset of radiation measurements. The goal of this part of the work is to investigate the usefulness of single sensor measurement for modeling PV output as single point measurements are more readily available. As using fewer sensors creates smoother fields we investigate the impact of reducing the number of sensors and the feasibility of using a smaller subset. The black line in Figure 3 shows how the ramps of a 30 MW plant would be distributed if we used a single sensor to determine the solar radiation incident on the plant. Apparently the single sensor based plant output does not match the multi-sensor plant output. We therefore investigate filtering methods to model such large 30 MW plants using a smaller set of solar radiation measurements.

Figure 1: GHI distribution from 17 GHI measurements at a site in Hawaii. The sensors are distributed over an approximately 1 square kilometer area and measurements are made every second.

Figure 2:  Cumulative Probability distribution of ramps in MW for power output at 60-second resolution for a 30 MW plant. 1 month of data from July 2010 was used.

Figure 3: 60 second ramp probability distribution for a single sensor compared to the power output created from multi-sensor high-density solar field. The solid blue line represents the multi-sensor array. The black line is represents the single-sensor with 60 second averaging. The dotted red and green lines represent 150 and 180 second averaging.