# Direct Solar Energy

3.5.3

Photovoltaic generation characteristics and the smoothing effect

At a specific location, the generation of electricity by a PV system varies systematically during a day and a year, but also randomly according to weather conditions. The variation of PV generation can, in some instances, have a large impact on voltage and power flow of the local transmission/ distribution system from the early penetration stage, and on supply- demand balance in a total power system operation in the high-penetration stage (see also Section 8.2.1 for a further discussion of solar electricity characteristics, and the implications of those characteristics for electricity market planning, operations, and infrastructure).

Various studies have been published on the impact of supply-demand balance for a power system with a critical constraint of PV systems inte- gration (Lee and Yamayee, 1981; Chalmers et al., 1985; Chowdhury and Rahman, 1988; Jewell and Unruh, 1990; Bouzguenda and Rahman, 1993; Asano et al., 1996). These studies generally conclude that the economic value of PV systems is significantly reduced at increasing levels of system penetration due to the high variability of PV. Today’s base-load generation has a limited ramp rate—the rate at which a generator can change its out- put—which limits the feasible penetration of PV systems. However, these studies generally lack high-time-resolution PV system output data from multiple sites. The total electricity generation of numerous PV systems in a broad area should have less random and fast variation—because the generation output variations of numerous PV systems have low correla- tion and cancel each other in a ‘smoothing effect’. The critical impact on supply-demand balance of power comes from the total generation of the PV systems within a power system (Piwko et al., 2007, 2010; Ogimoto et al., 2010).

Some approaches for analyzing the smoothing effect use modelling and measured data from around the world. Cloud models have been developed to estimate the smoothing effect of geographic diversity by considering regions ranging in size from 10 to 100,000 km^{2 }(Jewell and Ramakumar, 1987) and down to 0.2 km^{2 }(Kern and Russell, 1988). Using measured data, Kitamura (1999) proposed a set of specifications for describing fluctuations, considering three parameters: magnitude, duration of a transition between clear and cloudy, and speed of the transition, defined as the ratio of magnitude and duration; he evalu- ated the smoothing effect in a small area (0.1 km by 0.1 km). A similar approach, ‘ramp analysis’, was proposed by Beyer et al. (1991) and Scheffler (2002).

In a statistical approach, Otani et al. (1997) characterized irradiance data by the fluctuation factor using a high-pass filtered time series of solar irradiance. Woyte et al. (2001, 2007) analyzed the fluctuations of the instantaneous clearness index by means of a wavelet transform. To demonstrate the smoothing effect, Otani et al. (1998) demonstrated that the variability of sub-hourly irradiance even within a small area of 4 km by 4 km can be reduced due to geographic diversity. They analyzed the non-correlational irradiation/generation characteristics of several PV systems/sites that are dispersed spatially.

368

Chapter 3

Wiemken et al. (2001) used data from actual PV systems in Germany to demonstrate that five-minute ramps in normalized PV power output at one site may exceed ±50%, but that five-minute ramps in the nor- malized PV power output from 100 PV systems spread throughout the country never exceed ±5%. Ramachandran et al. (2004) analyzed the reduction in power output fluctuation for spatially dispersed PV systems and for different time periods, and they proposed a cluster model to represent very large numbers of small, geographically dispersed PV sys- tems. Results from Curtright and Apt (2008) based on three PV systems in Arizona indicate that 10-minute step changes in output can exceed 60% of PV capacity at individual sites, but that the maximum of the aggregate of three sites is reduced. Kawasaki et al. (2006) similarly analyzed the smoothing effect within a small (4 km by 4 km) network of irradiance sensors and concluded that the smoothing effect is most effective during times when the irradiance variability is most severe— particularly days characterized as partly cloudy.

Murata et al. (2009) developed and validated a method for estimating the variability of power output from PV plants dispersed over a wide area that is very similar to the methods used for wind by Ilex Energy Consulting Ltd et al. (2004) and Holttinen (2005). Mills and Wiser (2010) measured one-minute solar insolation for 23 sites in the USA and char- acterized the variability of PV with different degrees of geographic diversity, comparing the variability of PV to the variability of similarly sited wind. They determined that the relative aggregate variability of PV plants sited in a dense ten by ten array with 20-km spacing is six times less than the variability of a single site for variability on time scales of less than 15 minutes. They also found that for PV and wind plants similarly sited in a five by five grid with 50-km spacing, the variability of PV is only slightly more than the variability of wind on time scales of 5 to 15 minutes.

Oozeki et al. (2010) quantitatively evaluated the smoothing effect in a load-dispatch control area in Japan to determine the importance of data accumulation and analysis. The study also proposed a methodology to calculate the total PV output from a limited number of measurement data using Voronoi Tessellation. Marcos et al. (2010) analyzed one- second data collected throughout a year from six PV systems in Spain, ranging from 1 to 9.5 MW_{p}, totalling 18 MW. These studies concluded that over shorter and longer time scales, the level of variability is nearly identical because the aggregate fluctuation of PV systems spread over the large area depends on the correlation of the fluctuation between PV systems. The correlation of fluctuation, in turn, is a function both of the time scale and distance between PV systems. Variability is less correlated for PV systems that are further apart and for variability over shorter time scales.

Currently, however, not enough data on generation characteristics exist to evaluate the smoothing effect. Data collection from a sufficiently large number of sites (more than 1,000 sites and at distances of 2 to 200 km), periods and time resolution (one minute or less) had just begun in mid-2010 in several areas in the world. The smoothed generation characteristics of PV penetration considering area and multiple sites will