Elsevier

Solar Energy

Volume 86, Issue 8, August 2012, Pages 2170-2176
Solar Energy

Review
Short-term irradiance variability: Preliminary estimation of station pair correlation as a function of distance

https://doi.org/10.1016/j.solener.2012.02.027Get rights and content

Abstract

In this article, we report on the correlation between the irradiance variability observed at two neighboring sites as a function of their distance, and of the considered variability time scale. Correlation is the factor that determines whether the combined relative fluctuations of two solar systems add up when correlation is high, or attenuate when correlation is low.

Using one-dimensional virtual networks in 24 US locations and cloud motion derived from satellites as experimental evidence, we observe station pair correlations for distances ranging from 100 m to 100 km and from variability time scales ranging from 20 s to 15 min.

Within the limits of the assumptions from one-dimensional virtual networks, results show that the relationship between correlation, distance and time scale is predictable and largely independent of location and prevailing insolation conditions. Further, results indicate that the distance at which station pairs become uncorrelated is a quasi linear function of the considered time scale.

Highlights

► Site pair correlation of cloud transient variability predictably decreases as a function of distance. ► The decrease is inversely proportional to the considered data frequency. ► Short term variability with a time scale of less than 5 min is an issue for single systems, but should not be an issue at the scale of one city.

Introduction

The short-term variability of solar resource is perceived as a roadblock to the large scale deployment of solar power generation. This issue is the subject of several major research initiatives in the United States and internationally, (e.g., CSI, 2010, USDOE, 2009, BNL, 2010, SMUD, 2010, IEA, 2010).

In a recently published article, Hoff and Perez, 2010a, Hoff and Perez, 2010b advanced that the relative short-term variability of a fleet of identical PV generators decreases as the inverse of the square root of their number if the fluctuations of each system are uncorrelated. They defined relative short-term variability as the variability resulting from the fleet of systems, and quantified it by the standard deviation of the fleet’s time series of changes in power output, normalized to the fleet’s total capacity. More recently, Perez et al. (2011), building upon earlier work by Skartveit and Olseth (1992), showed that short-term variability for a single system at a given point in time could be estimated from hourly satellite-derived irradiances data such as Solar Anywhere (2010) or the NSRDB (1998–2005).

In this article we focus on station pairs, and investigate the correlation of their short-term variability as a function of their distance. A zero correlation would indicate that, per Hoff and Perez, 2010a, Hoff and Perez, 2010b, their cumulative relative variability will be 1/2 times their individual relative variability. Further, the possible existence of negative correlation at some key distance would indicate that fluctuations tend to cancel out, as hypothesized in Hoff and Perez’s optimum point.

Section snippets

Experimental data

Experimental measuring station pairs positioned at arbitrary distances and located in arbitrary climatic environments would constitute the ideal source of experimental data to undertake the present analysis. Unfortunately, this information is not fully available just yet. Although a few networks do exist where a partial validation of the present results will be possible (e.g., Kleissl, 2009), the necessary dense solar resource grids are on the drawing board or in the startup phase as of this

Results

The objective is to understand how station pair correlation varies as a function of distance and the considered sampling interval.

Starting with the observation of the relationship obtained from one day’s worth of observations at one of the virtual network, we proceed with analyzing the composite trend resulting from all the days analyzed at that same network location per Eq. (4), investigating how the single day’s relationship evolves. Finally we observe how the relationship further evolves

Discussion

The virtual network analysis undertaken here on a large array of climatic environments, weather drivers, and seasonal conditions leads to a remarkably well defined set of trends linking distance, fluctuation frequency and station pair correlation.

The evidence from this exhaustive analysis suggests that 20 s fluctuations become uncorrelated positively at a distance of less than 500 m. The distances are respectively 1 km, 4 km and 10 km for fluctuation time scales of 1, 5 and 15 min respectively.

The

Acknowledgements

This study was funded by Clean Power research under a California Solar Initiative (CSI) Grant Agreement titled “Advanced Modeling and Verification for High Penetration PV.” The California Public Utilities Commission is the Funding Approver, Itron is the Program Manager, and the California IOUs are the Funding Distributors.

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