Fast dynamic processes of solar radiation

Available online at www.sciencedirect.com

Solar Energy 84 (2010) 318–323 www.elsevier.com/locate/solener

Fast dynamic processes of solar radiation Teolan Tomson * Department of Materials Science, Tallinn University of Technology, Ehitajate tee 5, 19086 Tallinn, Estonia Received 28 January 2009; received in revised form 6 November 2009; accepted 29 November 2009

Communicated by: Associate Editor David Renne

Abstract This paper studies dynamic processes of fast-alternating solar radiation which are assessed by alternation of clouds. Most attention is devoted to clouds of type Cumulus Humilis, identified through visual recognition and/or a specially constructed automatic sensor. One second sampling period was used. Recorded data series were analyzed with regard to duration of illuminated ‘windows’ between shadows, their stochastic intervals, fronts and the magnitude of increments of solar irradiance. Ó 2009 Elsevier Ltd. All rights reserved. Keywords: Cumulus Humilis; Duration; Interval; Front and increment of solar radiation

1. Introduction In studying the correct functioning of a PV-array in combination with a battery and inverter, attention must be given to the dynamic behavior of the energy source. Likewise, the same principle applies to solar thermal systems, which perform under conditions of alternating radiation. They are cooled down and warmed up frequently, which increases losses. Fatigue of materials depends on the same alternating thermal processes, being a result of alternating radiation. The behavior of annual, monthly, daily and hourly averages of solar radiation is known in detail. Even minute-long averages have been studied to some extent (Gansler et al., 1995; Soubdhan and Feuillard, 2005; Tomson and Mellikov, 2004; Tomson and Tamm, 2006; Tovar et al., 1998). Lack of knowledge about faster processes of solar radiation in the second-long range has inspired the experimental study presented below. Over this range, diurnal and seasonal periodical processes have no meaning and may be eliminated. Therefore, the radiation relevant to this study can be considered a purely stochastic *

Tel.: +372 6203372; fax: +372 6203367. E-mail address: teolan@staff.ttu.ee

0038-092X/$ - see front matter Ó 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.solener.2009.11.013

phenomenon. The stochastic origin of radiation is caused by clouds, which will be evaluated from the point of view of their dynamic behavior, and the classification below differs from that used in atmospheric physics. All data used in the paper were observed or recorded at Tallinn University of Technology 59°230 N, 24°400 E during the summer season of 2008 (from May till August). The monitoring pyranometer used is a photoelectrical model from SolData Instruments (DK), which has a transient response of a millisecond or less (SolData Instruments, 2009). A recording (sampling) interval of 1 s was used. The data were stored in the data logger of a GRAPHTEC Corporation ‘Midilogger’ GL200. 2. Visual recognition of clouds Visual recognition of clouds is a rough means of assessing a situation in which fast changes of solar radiation may be expected and recorded. This method is preferred due to its simplicity as it may be used by everyone and everywhere. Unfortunately, the result is not accurate enough as we will see later. The conditions of the cloud cover were evaluated by two independent observers every noon following the classifica-

T. Tomson / Solar Energy 84 (2010) 318–323

319

Table 1 Conditions of the cloud cover. Description

Evaluation mark

Clear sky High turbidity or light (sparse) upper clouds Overcast or foggy Mainly cloudy with some cracks between them High Cumulus, moving slowly Low Cumulus Humilis, moving fast

0 1 2 3 4 5

tions outlined in Table 1. Situations ‘0’, ‘1’ and overcast clouds ‘2’ do not induce fast changes (high increments) of solar radiation, although solar radiation does always manifest small-scale fluctuations. Arbitrarily, we consider the global solar irradiance1 G(t) as having small-scale fluctuations if the increment of the solar irradiance is DG < 50 W m2 s1 for clear sky conditions and DG < 150 W m2 s1 (Tomson and Tamm, 2006) in overcast conditions. The increment of the solar irradiance is defined as the difference between its values in a sequence of recordings DG = Gn+1  Gn. A clear sky day has a low value of ratio between the standard deviation Gstdev and the average value Gaver of irradiance Gstdev/ Gaver < 1%. Fig. 1 shows examples: line 1 was measured on 27 June 2008 with parameters Gaver = 949.4 W m2; Gstdev = 1.33 W m2 and line 2 was measured on 26 May 2008 with parameters Gaver = 891.4 W m2; 2 Gstdev = 0.88 W m . Both of them were recorded with the 45° tilted surface facing due South. Both examples exhibit high frequency fluctuations. Under light cloud cover, small-scale fluctuations have a greater magnitude and a lower frequency as shown in Fig. 2. The ratio Gstdev/Gaver has a value in the range of a few per cent. Line 1 was recorded on 4 July 2008: Gaver = 295.4 W m2; Gstdev = 21.0 W m2; line 2 on 2 July 2008: Gaver = 576.5 W m2; Gstdev = 23.9 W m2. Under heavy cloud cover (with several cloud layers), Gaver < 100 W m2, small-scale fluctuations show a similar standard deviation as in the case of a clear sky. Large-scale increments may appear together with clouds of type ‘3’, alternating with cracks. High Cumulus clouds of type ‘4’ have abrupt edges and these induce large-scale increments with low (stochastic) frequency. Type ‘5’ low Cumulus Humilis clouds move fast and always induce high and frequent large-scale increments. The observations made during the summer season of 2008, from May till August, show a distribution of cloudiness as shown in Fig. 3. Tallinn has a marine climate where cloudy and overcast skies prevail, but the proportion of fast alternating clouds is also significant (13%). According to the observations (by different and independent observers), the share of days with alternating clouds (of types ‘3’, ‘4’ and ‘5’) was significantly lower (39% by

1 Here and below, we mean global solar irradiance G, unless stated otherwise.

Fig. 1. Small-scale fluctuations of the solar irradiance in clear sky conditions.

Fig. 2. Small-scale fluctuations of the solar irradiance under light cloud cover.

Fig. 3. Quality of clouds by observation.

the first and 7% by the second observer) than that discovered by the automatic sensor – 55%. The subjectivity of observers is high; also the frequency of observations (once per day) was too low. As technical problems were likely to be encountered due to large-scale fluctuations, our main attention turned to clouds of type Cumulus Humilis, Fig. 4. 3. Automatic sensor to detect fast-alternating radiation2 To increase the reliability of analysis a special automatic sensor was constructed. Its schematic diagram is presented in Fig. 5.

2 The author’s approach to using specialized hardware is based on his former experience with designing electronic equipment. The same problem can be solved with a standard PC and continuous recording, which is extended with specialized software to delete uninteresting data.

320

T. Tomson / Solar Energy 84 (2010) 318–323

Fig. 4. Example of the single-layer Cumulus Humilis.

186 files (534,582 points of sampled data) which are included in the analysis below. The real number of files is 30% bigger, but short (9 min) files were mostly deleted as they did not contain any useful information. The longest continuous recording lasted 5.4 h. The duration of continuous recording is classified and presented in Fig. 6. Fig. 7 shows the daily distribution from the moment of starting the recording. Noon is the most likely time to find alternating clouds, but not the only time. Increasing the number of recognitions per day should increase the trustworthiness of visual recordings. The position of the pyranometer used for data recording was tilted 45° and South facing in the month of May and June and horizontal in July and August. In its tilted position, the angle of incidence was lower and the recorded average values of irradiance and their increments were correspondingly higher. 5. Large increments of solar irradiance All small-scale fluctuations cause no problems for technological applications and therefore their exact analysis is not required. Large-scale fluctuations have a direct impact on technological applications and are studied in detail. An example is shown in Fig. 8. It was recorded on the horizon-

Fig. 5. Automatic sensor to control data logger with high resolution.

Recording starts:

share, %

15.0

10.0

5.0

18:00-19:00

16:00-17:00

14:00-15:00

0.0 12:00-13:00

During the four summer months (M, J, J, A) of 2008, the automatic recording of the global irradiance produced

20.0

10:00-11:00

4. Results of automatic recording

Fig. 6. Distribution of recorded files by their duration.

8:00-9:00

The automatic sensor has an analogue block and a digital block. An input signal is generated by the pyranometer P connected to a bridge which has resistive and inertial (low pass filter LPF) legs. The digital output signal of the analogue block is shaped by the threshold element ‘ ’. An output signal appears each time the instant value of solar irradiance increases sufficiently above its moving average value (the required difference being around 100 W m2). The digital block consists of a counter CT1 which saves the number of events (2 or 4) detected by the analogue block. The time generator G and time counter CT2 shape a control interval (9 min). If there is no critical number of events (say 2 or 4), the control trigger T saves its neutral position and counters CT1 and CT2 return to zero position. If the critical number of events has been detected, the control trigger switches ‘on’ in the data logger, collecting data with a sampling interval of 1 s. The data logger will be switched ‘off’ when and if, during the next control interval, no critical number of events appears. For as long as they are repeated, the data logger continues to record the solar irradiance.

Fig. 7. Distribution of the daily moment of start of the recording.

T. Tomson / Solar Energy 84 (2010) 318–323

321

Fig. 8. An example of large-scale fluctuations. Fig. 10. Frequency distribution of large increments during M–J (solid line) and J–A month (dashed line).

tal surface on 22 August 2008 and is here presented as a 3 h long fragment of the full 5.4 h recording with 1 s sampling periods. The average value is Gaver = 450.5 W m2 and the standard deviation is Gstdev = 232.1 W m2. They have a uniform order Gstdev/Gaver > 10%. The upper envelope of the recorded diagram is 700 W m2 and the lower envelope is 100 W m2. The instantaneous value of the irradiation oscillates between these envelope values. While a second layer of cloud exists, the third level (similar to an envelope) will appear between the said limits. The recorded example corresponds to the single-layer clouds Cumulus Humilis like those shown in Fig. 4. Such an alternating irradiance may be approximated by a stochastic telegraph signal (Morf, 1998). The said example (Fig. 8) was analyzed for the full range of increments (Fig. 9). Positive DG > 0 and negative increments DG < 0 have coinciding and exponential distribution laws of probability. Trend lines for these can be expressed as F(DG)  220exp(1.4DG). The F(DG) probability distribution laws will become highly significant, when calculating the combined influence of several PV-farms on a common grid. Solid lines DG > 0 and DG < 0 in Fig. 10 correspond to a tilt angle 45° (facing due South). The dashed lines presented in Fig. 10 and the solid lines in Fig. 9 correspond to the horizontal plane. From the diagram we can see that small-scale fluctuations do exist alongside large-scale fluctuations, and that the classification made above is a subjective act. All 186 recorded files were analyzed with regard to large increments DG > 100 W m2 s1. Fig. 10 shows the result of this analysis, which shows the analogous exponential probability distribution laws. The tilt angle of the trend lines differs

Fig. 9. Distribution of increments depending on their magnitude.

due to the different positions of the sensor (May–June: tilted 45°; July–August: horizontal). The large increments are most problematic because of their effect on materials or energy conversion technology. The largest increment of 705 W m2 s1 was recorded on 9 June 2008 at 12.36 solar time. 6. Fronts of solar irradiance The selected largest increment itself does not characterize the full magnitude of the changing irradiance. The magnitude of large-scale fluctuations is assessed by taking their positive and negative fronts. We define a (positive) front of changing irradiance as an event with a monotonous rise including at least one increment with a value DGmax > 50 W m2 s1. A negative front is defined analogously by a decreasing irradiance and it has to consist of at least one increment with a value DGmin < 50 W m2 s1. Therefore, solar irradiance is a process including positive and negative fronts and small-scale fluctuations in between them. The location of the maximum (minimum) increment in the front is a random event as shown in Fig. 11, where the maximum increments are plotted in bold. While small-scale increments precede or follow in sequence with a ‘large’ increment and the process is monotonous, we include all such increments together in the said front. A front starts and finishes when an increment with a backward sign appears in the sequence. The duration of a front is defined as the time interval between these boundaries (i.e. between the start and the

Fig. 11. Examples of positive fronts of irradiance on 22 August 2008.

322

T. Tomson / Solar Energy 84 (2010) 318–323

final moments). The probability frequency distribution law of the duration of fronts (close to a Weibull function, which has an empirical approximation R(x, a, b), where x = 1, a 2 {2.7  F(f)} and b = 1) for short and steep fronts is shown in Fig. 12. Automated selection of these boundaries (‘start’ and ‘final’) is complicated. Therefore a better approach had to be found, as described below. 7. Digitization of the recorded data series The duration of illuminated intervals (‘windows’ between clouds) and their ‘periodicity’, i.e. the time intervals between successive positive (or correspondingly negative) fronts may be selectively assessed while we transform a recorded ‘analogue’ data series G(t) into a digital form of existence G 2 {1, 0}, invariant with their real value. Such a series of digital numbers is a random telegraph signal. Fig. 13 shows a possible transformation of a fragment of the recorded example into a digital signal. Here, G(0, 1) = 1 while G(t) > Gaver, where Gaver is a moving average value of the irradiance. Correspondingly G(0, 1) = 0 while G(t) < Gaver. A problem exists for the calculation of the moving average value: how long should the averaging interval be? It is natural to use a correlation interval during which random values are statistically dependent. Due to the unstable structure of large fluctuations, this correlation interval is a time-dependent variable itself. Using a uniform averaging time interval over a long data series involves an error, the value of which cannot be assessed without a special investigation.

8. Stability of large-scale fluctuations The stability of fluctuations may be evaluated using the correlation interval of its autocorrelation function (ACF), Fig. 14. The bold line is calculated for a full 3 h long dataset. Other lines are calculated for one hour long fragments in such a way that every new one hour long data series is selected half an hour later. This means that diagram q(+1) is delayed 30 min in relation to diagram q(+0.5); that diagram q(+1.5) is delayed in relation to diagram q(+1) and so on. This analysis shows that the structure of large fluctuations is unstable. The same feature can be found when we analyze the (stochastic) frequency of fronts by the digitizing method described above. The frequency is defined as the number of fronts per unit time (min, h). We can see that the stability of fluctuations is low as the correlation interval s changes up to four times during a recording (5.4 h). The technology used for the ACF calculation and definitions of relevant notions are explained in (Tomson et al., 2008). In the investigation below a formal averaging interval of 1 h was used. 9. Analyzing the data series Digitized data series allow an analysis of the duration of illuminated ‘windows’ between clouds and their intervals

Fig. 14. Autocorrelation functions for the example Fig. 8.

800

duration, s

Fig. 12. Frequency distribution of (positive) fronts.

600 "window" 400

period

200

0 0

Fig. 13. An example of a digitalized data series.

50 100 sequence number of events

150

Fig. 15. Duration of illuminated ‘windows’ and their ‘periodicity’.

T. Tomson / Solar Energy 84 (2010) 318–323

323

(‘stochastic periods’). The result of analyzing the data (from 22nd August 2008) are shown in Fig. 15. The whole duration of the analyzed interval was 2.8 h, of which 63.5% were ‘windows’ with high radiation. Most of the periods and illuminated ‘windows’ are short: 2/3 of the ‘windows’ are shorter than 23 s and 1/3 of intervals are shorter than 65 s. No functional dependence on probabilities seems to exist for ‘windows’ and their intervals under the conditions of Cumulus Humilis clouds.

means that small-scale fluctuations always exist together with large-scale fluctuations.

10. Summary

Gansler, A., Beckman, W.A., Klein, S.A., 1995. Investigation of minute solar radiation data. Solar Energy 55, 21–27. Morf, H., 1998. The stochastic two-stage solar irradiance model (STIM). Solar Energy 62, 101–112. SolData Instruments, Silkeborg, Denmark, Personal consultation, 2009. Available from: . Soubdhan, T., Feuillard, T., 2005. Preliminary study of one minute solar radiation measurements under tropical climate, In: Proceedings of ISES SWC2005 on CD-ROM, Paper 1511 pdf. Tomson, T., Mellikov, E., 2004. Structure of solar radiation at high latitudes. In: Proceedings of EuroSun2004, PSEGmbH, Freiburg, vol. 3, pp. 3-899–3-904. Tomson, T., Russak, V., Kallis, A., 2008. Dynamic behavior of solar radiation. In: Badescu, V. (Ed.), Modeling Solar Radiation at the Earth’s Surface. Springer-Verlag, Berlin, Heidelberg, pp. 257–281. Tomson, T., Tamm, G., 2006. Short-term variability of solar radiation. Solar Energy 80, 600–606. Tovar, J., Alados-Arboledas, L., Olmo, F.J., 1998. One-minute global irradiance probability distributions conditioned to the optical air mass. Solar Energy 62, 387–393.

Visual recognition of clouds should be made two or three times per day to obtain trustworthy data on events of fast-alternating radiation. An automatic sensor based on the comparison between instantaneous and average values of solar irradiance is a good tool for finding and recording these events. Fast changes of solar radiation appear mostly while clouds are Cumulus Humilis and they are most probable around noon. There is no obvious functional dependence according to duration of shadows of clouds and their intervals. Fronts of shadows are misty without clear boundaries or form and the probability density of their duration can be described by a Weibull function. The speed of changing irradiance, i.e. its increments, has an exponential probability density and no boundary exists between small-scale and large-scale fluctuations. This

Acknowledgement The author thanks the Estonian Science Foundation, for their support under Grant 7332. References