Kelly - Solar Energy - Improved Photovoltaic Energy Output for Cloudy Conditions

Available online at www.sciencedirect.com

Solar Energy 83 (2009) 2092–2102 www.elsevier.com/locate/solener

Improved photovoltaic energy output for cloudy conditions with a solar tracking system
Nelson A. Kelly *, Thomas L. Gibson
General Motors R&D Center, 480-106-269, Chemical & Environmental Sciences Laboratory, 30500 Mound Road, Warren, MI 48090-9055, USA Received 30 October 2008; received in revised form 3 August 2009; accepted 19 August 2009 Available online 23 September 2009 Communicated by: Associate Editor David Renne

Abstract This work describes measurements of the solar irradiance made during cloudy periods in order to improve the amount of solar energy captured during such periods. It is well-known that 2-axis tracking, in which solar modules are pointed at the sun, improves the overall capture of solar energy by a given area of modules by 30–50% versus modules with a fixed tilt. On sunny days the direct sunshine accounts for up to 90% of the total solar energy, with the other 10% from diffuse (scattered) solar energy. However, during overcast conditions nearly all of the solar irradiance is diffuse radiation that is isotropically-distributed over the whole sky. An analysis of our data shows that during overcast conditions, tilting a solar module or sensor away from the zenith reduces the irradiance relative to a horizontal configuration, in which the sensor or module is pointed toward the zenith (horizontal module tilt), and thus receives the highest amount of this isotropically-distributed sky radiation. This observation led to an improved tracking algorithm in which a solar array would track the sun during cloud-free periods using 2-axis tracking, when the solar disk is visible, but go to a horizontal configuration when the sky becomes overcast. During cloudy periods we show that a horizontal module orientation increases the solar energy capture by nearly 50% compared to 2-axis solar tracking during the same period. Improving the harvesting of solar energy on cloudy days is important to using solar energy on a daily basis for fueling fuel-cell electric vehicles or charging extended-range electric vehicles because it improves the energy capture on the days with the lowest hydrogen generation, which in turn reduces the system size and cost. Ó 2009 Elsevier Ltd. All rights reserved.
Keywords: Solar energy; Photovoltaic; Solar tracking system; Diffuse irradiance; Hydrogen

1. Introduction Solar energy is a clean, renewable way to provide electrical power, as well as to boost the future hydrogen economy in the long-term via the electrolysis of water. At the GM R&D Center, we have investigated ways to optimize the solar to hydrogen process by photoelectrochemical and photovoltaic-electrolyzer (PV-electrolyzer) systems (Kelly and Gibson, 2006, 2008; Gibson and Kelly, 2008; Kelly et al., 2008). By improving the efficiency of the solarwater-splitting process, we can help to bring a solar-powered hydrogen home fueler for fuel-cell electric vehicles
*

Corresponding author. Tel.: +1 586 986 1623; fax: +1 586 986 1910. E-mail address: [email protected] (N.A. Kelly).

(FCEVs) closer to reality. Using renewably-generated hydrogen to power future FCEVs can eliminate air emissions from vehicles and contribute to the diversity of the possible sources of hydrogen (Burns et al., 2002). Previous PV-electrolyzer systems have only been developed for the purposes of demonstration and proof of concept due to their high system costs, system complexity, and, in some cases, low system efficiencies for generating the high-pressure hydrogen needed for hydrogen storage. Although it is feasible to optimize the efficiency of PV-electrolyzer systems for making hydrogen, there is also a need to improve the individual solar and electrolysis systems (Mann and Ivy, 2004). In this work, we describe a method to improve the PV output on cloudy days using a solar tracking system.

0038-092X/$ - see front matter Ó 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.solener.2009.08.009

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Photovoltaic modules are typically installed on structures such as homes or buildings using a fixed module orientation depending on the site characteristics and cost constraints. One orientation that is used on flat roofs is a horizontal (H) orientation in which the modules face straight up towards the zenith. Another configuration, that is the best overall fixed configuration for PV installations in North America, is one in which the modules face south and are tilted with respect to the ground at an angle equal to the site latitude (Lorenzo, 2003; Photovoltaic Systems Assistance Center, 1995); this is referred to as a latitude tilt. For example, in Detroit, with a latitude of approximately 42° north of the equator, the planar flat surface of the modules would be tilted at a 42° angle with respect to the ground. An ideal location for such a fixed system would be on a south-facing roof with a pitch approximately equal to the latitude tilt. The greatest amount of solar energy can be obtained for a given area of solar modules by using a mechanical tracking system so that the solar modules are always facing the sun (see Appendix A). This is referred to as 2-axis tracking since, as discussed next, two angles are needed to specify the location of the solar disk at any given time during the day. 1.1. Definition of solar angles to specify the position of the sun in the sky The sun’s location in the sky relative to a location on the surface of the earth can be specified by two angles (Iqbal, 1983). They are: (1) the solar altitude angle (a), and (2) the solar azimuthal angle (b). The angle a is the angle between the sun’s position and the horizontal plane of the earth’s surface, while the angle b specifies the angle between a vertical plane containing the solar disk and a line running due north. The solar altitude angle (the sun’s elevation with respect to the horizontal earth’s surface) is the compliment of the solar zenith angle (the angle between the sun and a line perpendicular to the earth’s surface). That is, a = 90° minus the solar zenith angle. The maximum solar altitude angle on a given day in the Northern Hemisphere occurs at solar noon, when the sun is directly south (i.e., b = 180°). On a sunny, cloud-free day, this will be the time of maximum solar irradiance (units of kW mÀ2). For the winter solstice in Detroit (approximately December 21), the maximum altitude angle is a = 24.2°, while for the summer solstice in Detroit (approximately June 21), the maximum solar altitude angle is a = 71.1° (US Naval Observatory). For Detroit at the time of the winter solstice, the sun rises at 8:00 AM at an azimuthal angle of 122° and sets at 5:00 PM with an azimuthal angle of 238°, moving over an azimuthal angle change of only 116°. At the time of the summer solstice in Detroit, the sun rises at 6:00 AM (daylight savings time) at an azimuthal angle of 57° and sets at 9:10 PM at an azimuthal angle of 303°, moving over an azimuthal angle change of 246°. A 2-axis PV tracking system orients PV modules so that they remain perpendicular to

the sun’s direct rays as the angles a and b change throughout the daylight period from sunrise to sunset at any given site. 1.2. The global solar irradiance and its components The total (global) solar irradiance (kW mÀ2) impinging on the horizontal surface of the earth is typically measured using pyranometers mounted horizontally to measure the irradiance over 2-p steradians (a hemisphere) Iqbal, 1983; Duffie and Beckman, 2006; National Solar Radiation Data Base (NSRDB); Wilcox, 2007; Stine and Geyer; Myers, 2005. This global horizontal radiation, Gh, is composed mainly of two components: They are: (1) beam (direct) horizontal radiation, Ibh, coming directly from the solar disk, and (2) sky (diffuse) horizontal radiation, Idh, that is first scattered by molecules and particles, including clouds (Lorenzo, 2003; Iqbal, 1983; Duffie and Beckman, 2006; National Solar Radiation Data Base (NSRDB); Wilcox, 2007; Stine and Geyer; Myers, 2005). This is expressed by the equation: Gh ¼ I bh þ I dh ð 1Þ

There is also some radiation that is reflected from the ground; this will be more important for tilted surfaces than for horizontal ones, and for simplicity is neglected here. Using a pyrheliometer with a narrow field of view that is mounted on a tracking mechanism such that it is pointed at the solar disk, researchers measure the beam normal irradiation, Ibn, which comprises the nearly parallel rays from the solar disk. The relationship between Ibh and Ibn is: I bh ¼ I bn  cosine ðHÞ ð 2Þ

where H is the angle between the solar disk and the normal to a horizontal surface, i.e., H is the solar zenith angle. This is referred to as the cosine response of a light sensor; a perfect sensor would have this cosine response (referred to as a perfect Lambertian response) for beam incidence angles from 0° to 90°. Thus, as per Eq. (2), for a solar ray striking a surface at angle of 90°, the angle H between the ray and a surface normal is 0°, and all of its energy would be transferred (cosine 90° = 1), while for a ray grazing the surface, the angle H between the ray and a surface normal is 90° and no energy would be transferred (cosine 90° = 0). Notice that for a horizontally-oriented surface, the azimuthal angle is irrelevant to specifying the angle of incidence of a direct solar ray; for such a surface H is equal to the complement of the solar altitude angle (90° À a). For a horizontally-oriented solar module the response to direct sunshine would thus be equal to Ibn  cosine (90° À a), where a is the solar altitude. Using the above, the global horizontal solar irradiance can be expressed using the well-known relationship: Gh ¼ I bn  cosine ðHÞ þ I dh ð 3Þ

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A 2-axis tracking system is most effective in increasing the solar energy harvest for direct radiation (no clouds) since it keeps H between the direct solar rays and the normal to solar modules at 0° so that the cosine (H) = 1. On cloud-free days 85–90% of the sun’s energy comes from the direct component, while the other 10–15% is diffuse radiation from the sky, mostly scattered from atmospheric aerosols (Gueymard et al., 2002). On cloudy days nearly all of the solar energy is diffuse. Since diffuse solar radiation is not aligned in a parallel fashion like direct radiation, tracking the sun does not increase and, as we will show later, dramatically decreases the solar energy from a PV system on cloudy days. Fig. 1 shows an example of the components of the solar insolation on a sunny and a cloudy-day for Detroit, MI obtained from the NSRDB (National Solar Radiation Data Base (NSRDB)). The NSRDB contains data and model-estimates of the global horizontal, beam normal, and diffuse horizontal insolation values; the beam horizontal (Ibh) value was calculated as the difference between the global horizontal and the diffuse horizontal radiation.

a

1000
Gh Ibn Idh Ibh

800
2

600

400

Notice in Fig. 1a that on a sunny day (June 2, 1986) the direct normal irradiance increases rapidly following sunrise and exceeds the global horizontal value throughout the day, except for a few hours around “solar noon”. The higher global horizontal near noon is due to: (1) the cosine factor is near 1 (Eq. (2)), and (2) the global horizontal insolation includes diffuse radiation while the beam normal does not. The beam normal insolation, Ibn, is similar to a 2-axis tracking value, Gn, except Ibn does not include the small contribution from diffuse radiation in the plane of the tracking detector, while 2-axis tracking includes a diffuse contribution. Nonetheless, the daily integrated beam normal insolation exceeds the global horizontal by 27% (Ibn = 10.9 kW h mÀ2, Gh = 8.6 kW h mÀ2). On a cloudy-day, Fig. 1b, the insolation terms that were largest in Fig. 1a are now the smallest, i.e., the direct insolation measurements, Ibn and Ibh. There is negligible beam radiation. Thus, nearly all (approximately 99%) of the global horizontal radiation is from the diffuse horizontal term. This illustrates that although a 2-axis tracking system, that efficiently collects beam solar radiation, will be ineffective on cloudy days. We will discuss solar radiation using both the solar irradiance (radiant power incident on a unit area on a surface, i.e., the rate at which energy falls on a unit surface in W mÀ2) and insolation (radiant energy incident on a unit surface area in W h mÀ2). The insolation is the solar irradiance integrated over a given time interval. On a cloud-free summer day the solar irradiance reaches approximately 1000 W mÀ2 at the surface of the earth. This “standard” irradiance of 1000 W mÀ2 is used in tests to rate the output of solar cells and modules, and is often referred to as “one sun”. 1.3. Maximizing the overall solar energy capture: 2-axis solar tracking

Insolation, Wh/m

200

0 4 6 8 10 12 14 16 18 20 22

Time of day

b

300
Gh Ibn Idh Ibh

250

Insolation, Wh/m

200

150

100

50

0 4 6 8 10 12 14 16 18 20 22

Time of day

Fig. 1. Global horizontal (Gh), beam normal (Ibn), diffuse horizontal (Idh), and beam horizontal (Ibh) insolation (hourly integrated irradiance) for Detroit on: (a) a sunny, (b) and a cloudy-day. The sunny day data is for June 2, 1986 and the cloudy-day data is from May 12, 1980 taken from the hourly NSRDB (National Solar Radiation Data Base (NSRDB)).

On a long-term basis, the most solar energy can be obtained from a given area of solar modules by having the modules mounted in a 2-axis tracking system (Appendix A). In such a tracking system, the modules are positioned such that the angle of incidence of incoming beam radiation with the solar module is 90°. This maximizes the “cosine” response to the beam radiation in Eq. (3). There are several types of 2-axis tracking systems (Photovoltaic Systems Assistance Center, 1991; Roth et al., 2005), ranging from systems that can accommodate over 18 m2 of typical solar modules (Array Technologies Inc.) to small trackers for mounting pyrheliometers (Yankee Environmental Systems Inc.). Some systems use active tracking methods, in which the motors and/or hydraulic devices are used to position the modules (Array Technologies Inc.), while others use passive methods, in which normally unused energy, such as heating of a fluid, is used to provide module alignment with the sun (Zomeworks Passive Energy Products). In addition, some use sensors with novel techniques to find the solar disk in the sky (Array

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Technologies Inc.), while others use computer programs that calculate the astronomical position of the sun (Yankee Environmental Systems Inc.; Amonix) from well-known algorithms (solar time-position calculations), and the calculations are used to control motors and gears that align the solar collector with the solar disk. Combinations of the various sub-systems are utilized in some tracking systems. Because up to 90% of the solar radiation is beam radiation sunny day, 2-axis tracking can provide a substantial gain in the solar energy harvested (Appendix A). Notice that the solar energy from a 2-axis tracking system is not identical to the Ibn measured with a pyrheliometer because a pyrheliometer does not measure any diffuse radiation, while the 2-axis tracking device includes some diffuse radiation (but not necessarily the horizontal diffuse radiation). The importance of this is that the data normally collected by solar researchers (Gh, Ibn, and Idh) is not sufficient to simply compute the 2-axis value for a solar system. However, there are algorithms for making this conversion, and in fact for calculating the energy on a surface with any tilt at a given time at a given site. In addition, there has been an extensive and on-going field of research on computing the theoretical clear-sky radiation (beam and diffuse), as well as models for cloudy and partly cloudy skies (Iqbal, 1983; Duffie and Beckman, 2006). In summary, the solar energy capture is maximized by a 2-axis tracking system because: (1) the solar energy is greatest on cloud-free days when there is ample direct sunshine, and (2) response of a solar module to a ray of light is proportional to the cosine of the angle between a line perpendicular to the module surface and a direct solar ray impinging on the surface (Iqbal, 1983; Duffie and Beckman, 2006; National Solar Radiation Data Base (NSRDB); Wilcox, 2007; Stine and Geyer; Myers, 2005). If the solar radiation is perpendicular to the surface, the maximum power for a given solar flux will be obtained (cosine 0° = 1). For solar radiation impinging at 90° from the normal, no power will be produced (cosine 90° = 0). As shown in Appendix A, based on an analysis of a large data base, a 2-axis tracking system increases the solar energy from a PV system by 52% versus a horizontal fixed tilt, and by 33% versus a latitude module tilt. As shown in Fig. 1, which uses data from the NSRDB, on cloudy days, beam solar radiation, Ibh and/or Ibn, is near zero, so 2-axis tracking will not produce more energy by capturing the direct radiation. Therefore, we sought to find a way to maximize the diffuse solar irradiance collected on cloudy days in order to increase the solar energy collected from a solar array on days with the lowest solar insolation. A 2-axis tracking PV system collects the solar irradiance coming directly from the sun as well as some diffuse irradiance (in essence, Gn, the global normal radiation). However, the diffuse radiation gathered by a 2-axis tracking system is typically not equal to the diffuse horizontal, Idh, since that quantity is exclusive to one condition; a horizon-

tally-oriented collector. Also notice that for clear-sky conditions Gn, the irradiance falling on a 2-axis tracking PV system is greater than Ibn, the beam normal irradiance, since Gn includes some diffuse radiation, while Ibn does not. 2. Experimental procedure 2.1. Measurement of 2-axis tracking and horizontal solar irradiance on cloudy days The measurements of the solar irradiance for different solar detector orientations on cloudy-days were made as follows. The horizontal (H) configuration measurements were made by placing the detectors or modules (described below) on a level horizontal surface. To measure the solar irradiance for the 2-axis tracking condition, the detectors were pointed directly toward the sun (DTS). On a cloudy-day, when the solar disk was obscured, this required knowledge of the solar angles defined in Fig. 1. These angles were obtained for a given measurement time from solar position computer programs (US Naval Observatory), as well as from mapping the solar position at given times on sunny days near in time to when the cloudy-condition measurements were made. A protractor, a yard stick, and a compass were used to set the detector orientation. The DTS measurements were not significantly influenced by small movements about the predetermined DTS position, so the results are relatively insensitive to errors in orientation about the DTS condition. 2.2. Solar irradiance measurement devices The solar irradiance (W mÀ2) and relative solar irradiance (ratio of output at different times or at different orientations) on different days and with different device orientations were measured with the series of detectors listed in Table 1. The Eppley pyranometer is widely used to measure solar irradiance (Iqbal, 1983; Duffie and Beckman, 2006) and its spectral response has been extensively characterized (Myers et al., 2002). It was calibrated by NREL in an outdoor comparison with solar standard pyranometers that they maintain (Broadband Outdoor Radiometer Calibration, referred to as BORCAL), so it could be used to measure the absolute value of the solar irradiance in our studies. The UDT photodiode was also calibrated by NREL using their indoor solar simulator (NREL Device Performance Measurement Site), so it also could be used to measure the absolute value of the solar irradiance. In comparisons with the Eppley radiometer using ambient solar irradiation at the GM R&D Center, the Eppley and UDT measurements exhibited excellent correlation and agreed in absolute value to within 4%. The Sharp and Sanyo “devices” were solar modules with areas of over 1 m2. The CT#1 and PF#3 sensors were also solar modules but they were small and could be held easily in one hand. The PF#3 sensor was flexible, so it was mounted onto a stiff sheet

2096 Table 1 Devices used to measure the solar irradiance. Device # 1 2 3 4 5 6
a b

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Device type Pyranometer c-Si photodiodea c-Si solar module c-Si and a-Si solar moduleb c-Si solar module a-Si solar module

Manufacturer Eppley Laboratories UDT Sensors, Inc. Sharp Inc. Sanyo Inc. Connecticut Solar Power Film

Model # 8–48, black and white PIN 10DP/SB NT-185U1 HIP-G751BA2 125 Â 227 mm size MPT3.6–75

Nomenclature Eppley UDT Sharp Sanyo CT#1 PF#3

Crystalline silicon (c-Si). Crystalline silicon (c-Si) and amorphous silicon (a-Si) layers.

of plastic so that it could not bend. Device numbers 1 and 2 in Table 1 were used to make absolute solar irradiance measurements, as well as relative measurements by orienting them at different tilt angles. Device numbers 3–6 in Table 1 were only used to make relative measurements at the orientations of interest. For the Eppley radiometer the solar irradiance was proportional to the mV output (10.54 mV = 1000 W mÀ2) signal measured with a Fluke model 179 true RMS multimeter. For all of the other sensors, the output was measured as the short-circuit current with model 77-III Fluke multi-meters. This direct measurement of the short-circuit current was in excellent agreement (4%) with that measured using an Agilent 34790A multi-meter capable of reading micro-volts (6.5 digit readout on a volt scale) across a 0.01 ohm current shunt to measure the short-circuit current. Notice that the cosine response of detectors predicts a weak dependence of the response for angular error (off-axis positioning) of up to 20°. For example, cosine (0°) = 1.00, cosine (5°) = 0.995, cosine (10°) = 0.985 and cosine (20°) = 0.940. So, for an error of 10° in lining up the detector towards the sun, the response will be reduced by 1.5%, and for an error of 20° the response will be reduced by 6%. 3. Results and discussion It is well established for sites across the US that 2-axis solar tracking increases the solar insolation by over 50% relative to that for PV modules with fixed horizontal orientation, and by over 30% relative to PV modules with a fixed latitude tilt (see Appendix A). This can be understood from the cosine response of flat-plate solar detectors and solar cells/modules to beam solar radiation on sunny days. Solar modules with a horizontal tilt (H) produce a fraction of the energy of modules pointed directly toward the sun (DTS) for cloud-free times with abundant direct sunshine; that fraction is approximately equal to the cosine of the angle H in Eq. (2). For example, consider a solar altitude of a = 45°, so that H in Eq. (2) is also 45° (H = 90 À a) for a horizontal surface. For clear conditions, with predominantly direct sunshine (with total diffuse irradiance of approximately 10% of the global solar irradiance, to a first approximation, it can be neglected), the H/DTS ratio would be approximately 0.71 (H = Gh % Ibh = Ibn  cosine

(45°) and DTS = Ibn, so H/DTS % cosine (45°) = 0.707). Thus, to a first approximation, a 2-axis tracking system would increase the solar energy capture by approximately 41% compared to a fixed horizontal module configuration for this example when the solar altitude is 45° and the sky is cloud-free. For solar altitudes less than 45° the 2-axis tracking advantage will be greater than that in the example, while for solar altitudes greater than 45° it will be less than that in the example. For sunny conditions, 2-axis tracking offers an advantage over any fixed solar module tilt, as discussed in Appendix A. The tracking advantage of a 2-axis tracking system versus a fixed horizontal module orientation is equal to ((DTS/H)-1). In terms of the H/DTS ratio we have chosen for analysis, the tracking advantage, TA, is: TA ¼ ð1-H=DTSÞ=ðH=DTSÞ ð 4Þ

For the example above, a sunny condition with a solar altitude angle of 45°, the TA would be equal to 0.41. Below we address the question of how a 2-axis tracking system affects the energy capture on cloudy days, when, as shown in Fig. 1b, nearly all of the solar irradiance is diffuse rather than beam irradiance. 3.1. The effect of solar tracking on cloudy days The data in Table 2 can be used to determine the effect of 2-axis tracking on cloudy days with little or no direct sunshine. Some tracking systems track the sun regardless of the sky condition (whether cloud-free or heavily overcast) by using a sun-pointing program to calculate the solar position (solar altitude angle, a, and solar azimuthal angle, b) and apparatus for positioning solar modules so that they face the solar disk. Note: this is the type of tracking used to compile the data utilized in preparing the NSRDB (National Solar Radiation Data Base (NSRDB); Wilcox, 2007), i.e., a tracking pyrheliometer, with the tracking controlled by an algorithm (to measure Ibn, together with a shading device and a pyranometer to measure Idh). The effect of such a tracking system on the solar irradiance was assessed by measuring the H/DTS ratio. Table 2 shows the results of 20 measurements of the H/ DTS ratio from six different sensors (Table 1) obtained on four overcast days during the fall of 2004 and spring of 2005 in Warren, MI. Recall that the DTS measurement is

N.A. Kelly, T.L. Gibson / Solar Energy 83 (2009) 2092–2102 Table 2 Measurements of the solar irradiance for a solar sensor with an horizontal (H) orientation as well as pointed directly toward the sun (DTS). Date 10-26-04 10-26-04 11-3-04 11-3-04 11-11-04 11-11-04 11-11-04 11-11-04 4-7-05 4-7-05 4-7-05 4-7-05 4-7-05 4-7-05 4-7-05 4-7-05 4-7-05 4-7-05 4-7-05 4-7-05 Mean Std. dev.
a b c d e

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Time of the daya 4:30 PM 4:30 PM 1:40 PM 1:40 PM 1:05 1:05 1:05 1:05 PM PM PM PM

Solar sensorb UDT Sharp UDT Eppley UDT Eppley Sharp Sanyo UDT UDT UDT UDT CT#1 PF#3 UDT CT#1 PF#3 UDT CT#1 PF#3

Solar irradiancec (WmÀ2) 129 136 193

H/DTS ratio 1.82 1.64 1.58 1.38 1.77 1.50 1.63 1.67 1.42 1.38 1.38 1.39 1.31 1.43 1.31 1.31 1.20 1.46 1.37 1.51 1.47 0.16

Solar altitude angle, a (°)d 19.1 29.0 28.8

Tracking advantagee À0.45 À0.39 À0.37 À0.27 À0.43 À0.33 À0.39 À0.40 À0.30 À0.28 À0.27 À0.28 À0.24 À0.30 À0.23 À0.24 À0.17 À0.32 À0.27 À0.34 À0.31 0.07

10:40 AM 11:10 AM 11:25 AM 1:00 PM 1:00 PM 1:00 PM 1:50 PM 1:50 PM 1:50 PM 3:20 PM 3:20 PM 3:20 PM

69 254 169 71

37.8 42.4 44.6 53.8

61

54.4

122

47.6

Local daylight saving time (applies to 10-26-04 and 4-7-05). See Table 1 for detector identification and characteristics. The “solar irradiance” was computed using the calibrated UDT sensor with an H orientation for the given time. The solar altitude angle was obtained from the US Naval Observatory web site. The “tracking advantage” was computed using Eq. (4).

equivalent to a 2-axis tracking measurement. As shown in the H/DTS ratio listed in Table 2, on cloudy days orienting the solar sensors horizontally (H) increases their output by a factor of 1.20–1.82 (mean ratio = 1.47 ± 0.16) compared to the directly toward the sun (DTS) orientation. This 47% average increase in energy with the H configuration over the DTS configuration is in marked contrast to the value in Appendix A, which shows that a 2-axis solar tracking system (attaining the DTS configuration) increases the PV solar output by approximately 52% versus the H configuration at 239 sites considered in the NSRDB over a 30-year analysis period (National Solar Radiation Data Base (NSRDB)). Thus, the overall H/DTS ratio is approximately 0.66 (1/1.52). In marked contrast, the results in Table 2 show that for overcast periods the H/DTS ratio averages 1.47. Clearly, although 2-axis tracking improves the overall energy capture, there are periods when, due to cloud cover, tracking the sun reduces the solar energy capture. This information can be used to design an improved tracking algorithm and system. In terms of the TA in Table 2, because all of the measurements were made with heavy overcast, there is a negative TA (a tracking disadvantage) ranging from À0.17 to À0.45 with a mean of À0.31. Thus, an open-loop tracker that follows the solar disk using an astronomically-based tracking algorithm (and apparatus to adjust the module tilt

angle based on the algorithm so that the modules are perpendicular to beam solar radiation) would have a TA averaging À0.31 versus a horizontal orientation during heavily overcast conditions. 3.2. Optimal module tilt on cloudy days We have found that pointing the modules towards the zenith (H condition) during overcast conditions results in significantly more solar irradiance than having the modules tilted towards the obscured sun (DTS condition). Moreover, it would be a simple matter to add some hardware and software to a conventional 2-axis tracking system so that it will extract the maximum energy from solar modules by tracking the sun on sunny days, but orienting the modules horizontally on cloudy days, or during shorter cloudy periods. The optimal configuration of this “2-mode” tracking system would require data collection and analysis, especially to design the system so that it did not keep shifting, and using energy to drive the motors, when fast-moving clouds caused rapidly changing solar irradiance. Our analysis has only investigated heavily overcast conditions, which are a worst-case scenario for the day-to-day utilization of solar energy. We envision using PV energy to drive the electrolysis of water to make hydrogen in a home refueling system for

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FCEVs. It is important to increase the solar energy available from a PV system on cloudy days because the system needs to be sized to produce enough hydrogen to fuel a FCEV on the days with the least sunshine (cloudy days), or the convenience of such a solar-powered system could be lost. Positioning the panels with an H configuration can provide 30–80% greater energy than tilting the panels toward the sun on cloudy days – a major improvement. On the other hand it is imperative to have the system produce the most energy on sunny days and partly sunny days, so a 2-axis tracking system is needed. Therefore, we propose a 2-axis tracking system that tracks the sun on days when direct sunshine is available, but goes to an H configuration when it is overcast. Determining the increase in total energy that can be gained on overcast days by using the H configuration will require additional data collected over a large number of days and meteorological conditions. However, based on the data in Table 2, it is apparent that when it is overcast and the solar irradiance is less than 250 W mÀ2, the H configuration is superior to the DTS configuration. An analysis of meteorological data (University of Utah) for Detroit, MI and Phoenix, AZ, in Fig. 2a shows that there are significant percentages of cloudy or partly cloudy days in both Detroit (79%) and even in Phoenix (42%). For cloudy days, Fig. 2b, the percentages are 50% for Detroit and 19% for Phoenix. Therefore, the advantages of an H solar module configuration for cloudy days or cloudy periods will be useful much of the time, and even at sites like Phoenix that are considered sunny.

a
Fraction, cloudy& partly cloudy days per month

1.00 0.90 0.80 0.70 0.60 0.50 0.40 0.30 0.20 0.10 0.00 1 2 3 4 5 6 7 8 9 10 11 12
Phoenix Detroit

Overall fraction
Phoenix = 0.42 Detroit = 0.79

Month of the year

b 0.80
Fraction of cloudy days per month
0.70 0.60 0.50 0.40 0.30 0.20 0.10 0.00
1 2 3 4 5 6 7 8 9 10 11 12 Phoenix Detroit

Overall fraction
Phoenix = 0.19 Detroit = 0.50

Month of the year

3.3. Comparison of the cloudy-day H/DTS ratio to predictions from the isotropic diffuse radiation model On mostly cloudy, and especially heavily overcast days, almost all of the solar irradiance is diffuse (Fig. 1b). The diffuse solar irradiance is more complicated to model and predict than clear-sky radiation because of the random and complex nature of cloud cover. One of the first models that predicted the angular dependence of diffuse radiation falling on surfaces tilted with respect to the horizontal position was Liu and Jordan’s Isotropic Diffuse Model (IDM) in which the sky is considered as a perfect irradiator, outputting solar radiation that is uniformly balanced over the whole sky (Liu and Jordan, 1963). That is, no beam irradiance from the solar disk has reached the earth’s surface; rather, the sun’s irradiance is uniformly distributed by the cloud deck. There are also anisotropic models (Kambezidis et al., 1994) that work better under certain cloud conditions, especially when there are bright spots in the clouds, but for heavy overcast conditions the anisotropic models reduce to the same form as the isotropic model (Lorenzo, 2003). The IDM has the mathematical formula: I H;diffuse ¼ I dh  ð1 þ cosine ðHÞÞ=2Þ ð5Þ

Fig. 2. Fraction of (a) cloudy or partly cloudy days in Phoenix and Detroit, (b) cloudy days in Phoenix and Detroit. The standard meteorological definitions of the terms, from the US National Weather Service, are: (1) cloudy – 7/8 of the sky is covered by clouds, and (2) partly cloudy – between 3/8 and 5/8 of the sky is covered by clouds. The data is from the University of Utah meteorology site.

where IH,diffuse is the measured irradiance at a tilt angle H from the horizontal and Idh is the horizontally-measured diffuse radiation (solar disk shaded). Our measurement (during heavy overcast) of the H irradiance is Idh in the model and our measurement of DTS is equivalent to IH,diffuse, in the model, where the angle H in Eq. (5) is equal to the complement of the solar altitude angle (90 À a) in Table 2 for the DTS condition. Thus, in our measurements H/DTS should vary as the inverse of (1 + cosine (H))/2). Fig. 3 shows a plot of the inverse of (1 + cosine (H))/2) versus H as H varies from 0 to 90°, together with the measured values of H/DTS from Table 2. The model and the data show the same trend, but clearly the data predicts higher values for the angular dependence of the diffuse irradiance than the model. One possible reason for this is the effect of buildings above the horizon (which lowered the DTS value). We plan to collect a larger data base using several 10-module solar arrays at the GM Proving Ground (Kelly et al., 2008) to further test the IDM by determining the H/DTS ratio under a wider variety of conditions than experienced in the data collection for Table 2.

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2.0
Model Eppley

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1.8

UDT Sharp Sanyo

1.6

CT#1 PF#3

1.4

1.2

Three points here

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0 10 20 30 40 50 60 70 80 90

Sensor tilt angle, degrees

Fig. 3. Measured (Table 2) and modeled H/DTS ratio as a function of the sensor (or module) tilt angle with respect to the horizontal (tilt angle of 0° = horizontal). The model used for the H/DTS ratio is the Isotropic Diffuse Model (Eq. (5)), commonly called the Liu–Jordan model (Kambezidis et al., 1994).

3.4. Embodiments of a 2-axis solar tracking system with enhanced energy output on cloudy days A PV system will capture the most energy using a tracking system, preferably a 2-axis tracking system, since tracking systems maximize the energy capture for a given area of the PV modules during conditions with predominantly direct sunshine. Such systems can be augmented, using the inventive concept discovered in this work, in order to increase the capture of solar energy on cloudy days. Several possible embodiments of such a combined system are described below. The following system embodiments apply to flat solar modules, and do not apply to concentrating systems, requiring beam solar irradiance that is negligible on cloudy days. 3.4.1. Enhanced tracking system number 1 In the simplest embodiment of the cloud-optimized tracking system, historical measurements of the solar irradiance at the site of interest would be used to manage the tilt of a set of solar modules. Whenever the measured solar irradiance is below a predetermined value, relative to the clear-sky value, the modules would be moved to a horizontal position. Solar irradiance measurements at the predetermined low levels will occur due to wide-spread cloud cover of the sky. Whenever the measured solar irradiance exceeds the predetermined minimum value for the location, the module would be positioned according to 2-axis solar tracking for the location, day of year, and time of day using well-known sun-pointing programs. 3.4.2. Enhanced tracking system number 2 A second embodiment, which is very likely the preferred embodiment of our cloud-optimized tracker, would use an active (mechanized) 2-axis tracking system, such as those made by Array Technologies Inc., with the following

additions: (1) it would have one small (UDT type) solar cell fixed horizontally (H), and (2) another fixed with a southfacing latitude tilt (L). At times when there was direct sunshine, the L sensor would have a greater output than the H sensor, and the 2-axis tracking system would align the solar panels with the sun using well-known technologies and algorithms for such tracking. When H > L by some predetermined value, say H > 1.3 Â L, a signal would be generated which would cause the solar tracking motors to position the solar modules to face up towards the sky (horizontal). This would presumably be at times when there was near complete cloud cover. In order to have a system with minimal hydrogen storage and reduced cost, it is important to improve the solar hydrogen system’s output on cloudy days when less solar energy is available. In Detroit, approximately 50% of the days are cloudy (Fig. 2b) and the average increase in the H/DTS ratio for the cloudy periods, based on the results in Table 2, is approximately 50%. Therefore our tracking system could increase the collected solar energy by approximately 25%. This increase in solar energy collection in Detroit occurs when additional energy is most needed due to the decreased overall solar irradiance on cloudy days. If the solar array was providing energy to produce hydrogen from water electrolysis, and if the hydrogen was being used to provide most or all of the hydrogen to refuel a FCEV, then the PV system could be sized with less PV area and still make enough hydrogen on cloudy days. On sunny days in the summer or winter the excess energy produced by the PV system could be used to power the system owner’s home electrical needs or be sold back to the utility company. 3.4.3. Enhanced tracking system number 3 A third embodiment of the optimized tracking system utilizes two solar radiation sensors, mounted horizontally, to determine when to switch from 2-axis solar tracking to the horizontal mode. This method measures the global, beam, and diffuse radiation in order to determine when the modules should stop tracking the solar disk and instead attain a horizontal tilt. One sensor (sensor 1) is shaded from beam normal (or even the beam horizontal) radiation from the solar disk and measures the diffuse horizontal radiation. This can be accomplished with a shadow band that shades sensor 1 from direct sunshine as the sun moves across the sky or with a small shading disk attached to a small 2-axis tracker. The other sensor (sensor 2) is not shaded and measures the global horizontal radiation. The difference between the two sensors is the beam (normal or horizontal) radiation from the sun. A commercially available product that makes measurements of the global horizontal, beam normal, and diffuse horizontal solar components using a single detector is available from Yankee Environmental Systems, Inc., and is called a Single Detector Rotating Shadow Band Radiometer (SDR-1). When the sky is heavily overcast, the beam normal component of the solar radiation is near zero. For such times an array

H/DTS ratio

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of solar modules would be oriented horizontally to capture the most solar energy under heavily overcast conditions. When the beam normal component is significant, the regular 2-axis tracking of the sun by the array of solar modules would take place, to capture the most solar energy under sunny or partly cloudy conditions. 3.4.4. Embodiment of the invention for a 1-axis tracking system Many tracking systems designed for large solar installations use 1-axis tracking (SunPower Inc.) because it is: (1) simpler in both mechanical design and the ease minimizing shadowing between a large number of arrays, (2) less expensive, and (3) realizes approximately 90% of the 2-axis improvement over a fixed tilt. Our method of going to the H configuration on cloudy days or during cloudy periods could also be achieved with a 1-axis tracking system, since it can attain a 0° tilt (H configuration). That is, the 1-axis tracker would tilt the solar modules during periods with significant direct sunshine, but go to an H configuration during cloudy periods. The decision on when to switch from one mode to the other would utilize similar sensors and algorithms to determine when it is overcast as the embodiments for the 2-axis system. 3.5. Impetus for improving the capture of solar energy on cloudy days The importance of improving the solar energy output on cloudy days is that it reduces the system size and cost if the system is sized based on producing sufficient output on the worst solar days. Suppose for example, that a solar system is designed to produce, on average, sufficient solar energy to generate 0.5 kg of hydrogen per day via the electrolysis of water. This could be part of a home hydrogen fueling system for FCEV, and 0.5 kg of hydrogen would be sufficient to drive such a vehicle on an average daily commute of 30 miles (Kelly et al., 2008). On a sunny day the system will make more than that amount of hydrogen and on a cloudy day it will make less. In particular, on short, cloudy winter days the system will make much less that the average amount, while even on the longest sunniest summer day it will make no more than twice the average amount. Ideally, the H2 storage system must be able to hold enough hydrogen to supply the vehicle for a few bad days in a row – this is like the autonomy built into an off-grid solar system that uses batteries to store solar energy. Of course the vehicle can occasionally use the centralized hydrogen dispensing, but this is to be avoided as much as possible to maximize the use (convenience and cost) of the solar home fueling system. Therefore, improving the solar energy capture on the worst days is important to try to level the system output as much as possible. Improving the solar energy capture on cloudy days has received little attention; rather, the emphasis has been on maximizing the output on sunny days.

4. Summary A 2-axis tracking system works best on sunny days since it improves the collection of beam solar radiation, and worst on cloudy days when diffuse solar radiation predominates. Utilization of a tracking system will affect the size and cost of a PV system used to electrolyze water to produce hydrogen for a fuel-cell electric vehicle (FCEV) in a home hydrogen fueling system. A PV system can be the major cost item for such a system, especially in cloudy areas where a larger PV system is needed for a given amount of solar energy. In order to reduce the cost of the PV system, it would be very beneficial to boost the solar output on cloudy days. Unfortunately, this cannot be done using solar concentrators, since they can only focus direct (parallel) rays from the sun. We have shown that it is possible to obtain significant improvements in the solar energy captured by a solar array on cloudy days by orienting the solar modules horizontally (toward the zenith). This can be important for a solar-driven hydrogen fueling system in which an even day-to-day hydrogen production is desired. Our results also have more general applicability to optimizing the capture of solar energy for applications other than powering hydrogen production for FCEV or charging batteries in an extended range electric vehicle (EREV). Solar energy would still exhibit a seasonal as well as a day-to-day variation, but the dramatic decrease on heavily overcast days would be somewhat mitigated by the optimal tilt for such days outlined in this work. A 2-axis tracking system has well-known properties of improving the solar energy capture by a given area of solar modules. Including some hardware and an algorithm that we described would be a small addition to a 2-axis tracking system that would improve its performance on cloudy days. Several embodiments for such a system were described. 5. Conclusions

1. For cloudy conditions, especially for heavy overcast, orienting solar modules toward the zenith (a horizontal tilt) captures the most solar energy, i.e., approximately 50% more than that for a system that simply tracks the sun’s path through the sky every day regardless of the sky conditions. It is important to take advantage of this potential for increasing the solar energy capture on cloudy days because solar systems are often designed to be able to supply enough energy for the worst days. In particular, the dramatic improvement on cloudy days is especially useful for a home fuel-cell electric vehicle (FCEV) fueling system that needs to supply hydrogen for daily commuting on a continuous basis throughout the year. 2. For sunny conditions, a system that orients solar modules so that they are perpendicular to the direct rays from the sun, a so-called 2-axis tracking system, produces the most solar energy for a given photovoltaic

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module area, i.e., 30–50% more solar energy than a PV system with a fixed tilt. However, our measurements show that such solar tracking dramatically decreases the solar energy output for cloudy conditions. 3. An optimized solar energy system would utilize 2-axis solar tracking during sunny conditions to capture the beam irradiance, but orient the modules toward the zenith for cloudy conditions, to capture the isotropically-distributed diffuse solar irradiance emanating from the clouds. In the past, the emphasis has been on optimizing the capture of beam solar radiation – by far the largest overall component of the solar irradiance. However, maximizing the capture of diffuse solar radiation is important for several reasons, including minimizing the system storage (to have enough energy to get by during “bad” solar periods), and leveling the day-to-day system fluctuations. 4. A simple model for diffuse radiation, referred to as the Isotropic Diffuse Model, agrees qualitatively with the angular dependence that we measure for the horizontal/2-axis tracking irradiance ratio on cloudy days. However, it predicts a lesser dependence for the magnitude of this ratio than we measured. 5. We propose three embodiments for an optimized tracking system that uses simple algorithms and sensors to determine when it is cloudy, and then orients the solar modules toward the zenith for maximum solar system performance the during periods of cloud cover.

2.50

Phoenix ratio = 1.56 Detroit ratio = 1.46

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0.00 Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec

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Fig. A1. The ratio of the peak sun hours (PSH = the number of hours per day with a solar irradiance of 1000 W mÀ2) for Detroit and Phoenix with a 2-axis tracking versus a horizontal orientation (tilt = 0°) for PV modules. The data is from the NSRDB (National Solar Radiation Data Base (NSRDB)).

Acknowledgments The authors thank Dr. Daryl Myers and Dr. Thomas Moriarity of NREL for calibrating our Eppley radiometer and UDT solar cell, respectively. Appendix A. Increase in solar energy capture using 2-axis tracking versus a fixed solar module tilt Using the National Solar Radiation Data Base (NSRDB) we can assess the effect of a 2-axis tracking system on the collection of solar energy using solar arrays. The NSRDB has solar data and model predictions for 239 sites across the US plus Guam and Puerto Rico for a variety of fixed and tracking solar configurations based on an analysis of data from 1961–1990 (National Solar Radiation Data Base (NSRDB)). The configurations of
Table A1 Ratio of annual insolation for a 2-axis tracking system to a fixed module tilt for a horizontal and a latitude tilt. Values are based on 30 years of measurements and modeling in NSRDB (1961–1990) for 239 sites. 2-Axis/horizontal Average Std. dev. Minimum Maximum 1.52 0.113 1.30 2.00 2-Axis/latitude tilt 1.33 0.045 1.20 1.50

most interest to us are a fixed horizontal (such as on a flat roof), a latitude tilt (approximating a sloped roof facing south – this is the optimal fixed tilt, or very close to it), and 2-axis tracking (this is the configuration that will yield the most solar energy). For all 239 sites the ratio of the average solar insolation (units of kW h mÀ2 dayÀ1) for a 2-axis tracking system to that for horizontal and latitude tilt solar module configurations was computed using the annual average for the 30-year period. Table A1 shows a statistical summary of that ratio. As can be seen in Table A1, the 2-axis tracking increases the solar energy collected by a solar array with a given area by 52% compared to a system with a horizontal fixed tilt, and by 33% compared to an array with a latitude tilt. This increase in solar energy collection can justify the added expense of the 2-axis tracking. The 2-axis tracking values used in the computations in the table are for a system that tracks the sun regardless of the presence of clouds, a socalled “time-position” system. Note: 2-axis tracking solar irradiance = Gn > Ibn as discussed in the text. A comparison of the seasonal effects of a 2-axis tracking system versus a horizontal fixed configuration is shown in Fig. A1. For a given month, the ratio of the 2-axis solar insolation to that for a horizontal orientation varied from 1.32 in the summer to 1.94 in the winter in Detroit, with a mean over the whole year of 1.46. That ratio for Phoenix varied from 1.39 in the summer to 2.10 in the winter with an overall annual mean of 1.56. Thus, comparing two sites with very different solar availability, the overall increase in solar energy by using a 2-axis tracking system versus a horizontal configuration varied from 1.46 to 1.56. Clearly, the 2-axis tracking system provides a dramatic overall increase in the solar energy capture for a given PV system area. References
Amonix. Available from: <http://www.amonix.com/>. Array Technologies Inc., Wattsun Solar Trackers. Available from: <http://www.wattsun.com/>.

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