# 11.1 Model linking solar intermittency with generation output

Power fluctuations have been analysed in [1] and [74] in terms of power spectral density (PSD), that is in the frequency domain, using two months of 10-second data and two years of 10-minute data from a 4.6MWp PV array and a 135kWp sub-array within it. The power spectral density of the output of large-scale PV can provide insight into the character of both cyclic (daily, seasonal) and non-cyclic (weather-related) fluctuations associated with array output [75]. Power spectral analysis can indicate the type of firm power or demand response appropriate to compliment PV including required ramp rate [76]. The main conclusion drawn from these studies has been that the larger the PV plant, the greater the attenuation of high frequencies [75].

Our work is based on ten months of 10-second data of power output and irradiance from the Desert Knowledge Australia Solar Centre (DKASC) site in Alice Springs. Figure 138 shows the irradiance and the output power recorded for a 15-minute period around midday at the DKASC on 27 January, 2011. Both signals have been normalised, the irradiance by 1000W/m^{2} and the power output by total PV rating (196kW). As expected, the power curve is smoother than the irradiance curve, because of the larger size of the PV plant when compared with the discrete character of the irradiance sensor. This is because the larger the size of the PV plant, the longer it takes for the cloud cover spread to shade the entire field. The PV plant power output can be described as the signal output of a low-pass filter where the input signal is the incident irradiance [77]. This correlation between the irradiance and power output can somewhat be seen in Figure 138. It is a first order filter whose pole value is a function of the PV plant area.

Figure 139 shows the Discrete Fourier Transform (DFT) of the irradiance signal recorded over ten months from October 2010 till August 2011 at the DKASC, computed through a Fast Fourier Transform (FFT) algorithm presented as a Bode (magnitude) plot. The daily solar resource cycle is evidenced by a peak at 24 hours, indicated in Figure 139 by a dashed vertical line at *log _{10}f =-4.93 (f* = 1.15 x 10-5 Hz). The frequency response for irradiance fluctuations has a characteristic slope of -0.72 (green line).

The same frequency domain analysis has been applied to the PV plant output power data recorded during the ten month period. Figure 140 shows the spectra of the power fluctuations using 10-second resolution data. The DKASC occupies approximately 4.14 hectares. The power spectrum can be described as two linear regions well fitted by functions given in (1) and (2) with characteristic slopes of -0.72 (solid green line) and -1.38 (dashed green line) respectively. The cross-point defines the cut-off frequency. Therefore, regarding power fluctuations, the PV plant size can be interpreted as a first order low-pass filter for the irradiance data. From this analysis, the cut-off frequency for the PV plant at DKASC was found to be 0.0055Hz *(log _{10}f* = -2.26) which agrees well with observations made by the authors in [77]. This cut-off frequency is indicated by a dashed vertical line in the power spectrum in Figure 140.

1og_{10}*(magnitu de)* = -0.721og _{10}( *freq)* + 0.22 (1)

*1og _{10}(magnitude) =* -1.381og

_{10}(freq)-

_{}1.26(1) (2)

The authors in [77] have undertaken a similar exercise for several PV plants which have different areas and rated power sizes. The cut-off frequencies for PV plants of different sizes were found and a relationship between the cut-off frequency and size of a PV plant was determined by a function given in (3). It was established from the analysis of cut-off frequency values that the main power fluctuation smoothing factor is the plant area rather than its rated power.

*f _{c} = a x S^{b}* (3)

where *f _{c}* is the cut-off frequency in Hz,

*S*is the PV plant size in hectares,

*a*= 0.0204 and

*b*= -0.4997.

According to (3), the cut-off frequency for the PV plant at the DKASC is 0.01 Hz *(log _{10}f* = -2.00). It should be noted that the DKASC consists of different types of solar panels, some with single- and others with double-axis tracking, with non-uniform ground coverage. The PV plant analysed in [77] involved arrays of the same type with single-axis tracking and a uniform ground coverage.

Using the developed model, the power output of an existing or proposed PV plant can now be obtained via simulation for measurements of a given irradiance time series. A graphical user interface (GUI) for the developed model can be seen in Appendix B. Figure 141 shows simulated and actual real power data for two consecutive days, 17 and 18 February 2011. The actual power output is shown in green, while the simulated output power is shown in red. Figure 142 shows the actual versus simulated power output over a five-hour period on 17 February 2011. The similarity between the actual and predicted output power is clearly observed, indicating that the simulation model developed is valid.

Similar work was carried out on two weeks of 5-second data of power output and irradiance from the CSIRO Energy Centre office building rooftop PV system in Newcastle. Figure 143 shows the DFT of the irradiance signal recorded over a two-week period in October 2011 at the CSIRO Energy Centre, computed through a FFT algorithm. A peak at 24 hours is again seen in the DFT plot representing the daily solar resource cycle. Similar to the DKASC, the same frequency domain analysis was applied to the 22 kW PV plant output power data during the two-week period. Figure 144 shows the spectra of the power fluctuations using 5-second resolution data. In this case, due to the significantly smaller size of the CSIRO’s office building PV system, a roll-off is not observed in the power spectra. The power spectra can be described as one linear region with characteristic slope of -0.93 (solid green line), which is the same as that for the irradiance spectra. Therefore, it can be said that a linear conversion model of irradiance to PV power output can be applied for small-scale PV systems like the one at CSIRO to predict their power output. Figure 145 shows the actual and simulated power data for two intermittent days where the power was predicted using a linear conversion model. The actual power output is shown in green while the simulated output power is shown in red.

The irradiance-power conversion model developed here is most applicable to large-scale PV systems where the PV plant power output is smoother than the irradiance signal and can be described more appropriately as the signal output of a low-pass filter whose input signal is the incident irradiance. Irradiance and power output data from the 1.22 MW PV plant at The University of Queensland was also obtained with a resolution of 1-minute but was not analysed using this model as the resolution of the data is not high enough for this particular analysis.

The model developed in this project can be used to serve several different purposes including:

- simulation of power fluctuations in any power network with PV plants of various sizes
- determination of energy storage or ancillary services requirement for a PV plant that is yet to be built. Solar irradiance data from the proposed site need to be obtained and used as input to the model for prediction of intermittent generation ramp rates, the likelihood of occurrence and the timescales over which they occur
- prediction of more accurate solar energy output, with a better estimated measure of intermittency at various timescales, using solar forecast data for potential PV plant sites.

The following section of this report includes a discussion of CSIRO’s work on predicting solar irradiance with a two-hour forecast window using neural network theory.