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Invited paper presented at the SPIE Great Lakes Photonics Symposium, June 7 – 11, 2004, Cleveland, Ohio.

HIGH-ALTITUDE AIR MASS ZERO CALIBRATION OF SOLAR CELLS[1]

Ali Mirza and James R. Woodyard

Department of Electrical and Computer Engineering

Wayne State University

Detroit, MI

ABSTRACT

Air mass zero (AM0) calibration of solar cells has been carried out for several years using methods that employ aircraft and large balloons. The methods are costly and can be carried out only at certain times of the year. A low cost method is under development in our laboratory that employs an approximately six-foot diameter helium-filled extensible balloon, suntracker and state-of-the-art communication technologies. The goal of the program is to calibrate multi-junction solar cells in the stratosphere under near air mass zero conditions.

The scientific package weighs less than six pounds and includes a suntracker, two global positioning system (GPS) receivers, two transmitters, batteries, video camera and antennas. One transmitter is used to downlink video data and the other packet data. Each transmitter is in a separate system that includes a GPS receiver, battery pack and supporting electronics. Two separate downlink systems are used to increase the chances of retrieving the package in the event one of the systems fails.

The Suntracker has two motor assemblies, collimator, electronics and a solar cell. Each motor assembly has a motor, gearbox and encoder that are used along with three microprocessors, software and associated electronics to point the collimator at the sun as the balloon ascends. One motor assembly is used to rotate the collimator in the altitude direction and the other in the bearing direction. The collimator is 4.0 inches long and has an aperture measuring 1.0 x 1.0 in² mounted on one end. The aperture limits the collimator field of view to about one degree and prevents sunlight reflected from the balloon, clouds and earth light to be incident on the solar cell. A 0.787 X 0.787 in² solar cell is soldered to a copper plate that is attached to the other end of the collimator. A thermistor is bonded to the back of the copper plate and used to determine the temperature of the solar cell.

Data are downlinked to both mobile and base stations during the flight; data include cell short-circuit current, cell temperature, electronics module temperature, reference voltage, atmospheric pressure, video and GPS information. The transmitters operate on 70-centimeter and 2-meter bands at frequencies of 439.25 and 144.10 MHz, respectively. The 70-centimeter band is used to downlink real-time video that shows the operation of the suntracker throughout the flight. The video signal is processed by a down converter and saved on videotape with a video recording unit. The 2-meter band is used to downlink packet data in AX.25 format; the data are processed by a terminal node controller and saved on the disk drive of a personal computer (PC). The mobile station also has a GPS receiver interfaced to a PC. The PC is used along with the downlinked packet data and mapping and balloon-trajectory software in the retrieval of the scientific package.

Seven flights have been attempted at various times of the year and under a variety of launch conditions. Flight durations were between three and four hours and ranges between 40 and 187 miles. Altitudes between 87,000 and 114,000 feet and air masses as low as 0.03 have been achieved. Solar cell calibrations were carried out using Langley plots and laboratory-based temperature measurements. Calibration results agree within 0.2 % from flight to flight as well as with NASA’s aircraft calibration method. The details of the system will be described with emphasis on the optics of the measurements.

INTRODUCTION

It is important in characterizing solar cells for use in space-power applications that the spectral irradiance of the calibration-light source is within a percent of the spectral irradiance of air mass zero conditions (AM0). Spectral irradiance differences greater than a few percent can result in calibration errors; the magnitude of the errors depends on the structure of the solar cell. In the case of single-junction cells, the current-voltage characteristics are not very sensitive to small differences in the spectral irradiances of calibration-light sources because the spectral response is not sensitive to spectral irradiance. Figure 1 shows the solar irradiance incident on a single-junction solar cell. The light injects electron-hole pairs which in turn produces a current in the single junction. The current under AM0 normal incidence with the cell operating at a voltage is given by

(1)

where is the absolute AM0 spectral irradiance of sunlight and is the spectral response of the cell at wavelength and voltage . In the ideal case, the spectral response is independent of the irradiance of the light source. The spectral response depends on the opto-electronic properties of the materials used in the fabrication of the cell that include, but are not limited to, the wavelength dependence of the optical absorption coefficient; optical band gap, material thickness, doping, temperature and quality; and carrier mobility and lifetime. andare the lower and upper cut-off wavelength values where the spectral response no longer contributes to cell current.

The spectral irradiance of laboratory-based solar simulators is different than the AM0 spectral irradiance. The simulator is set to “AM0” intensity by adjusting the intensity to produce the short-circuit current in a standard cell, i.e., a cell calibrated under AM0 conditions. This approach may be used because the spectral response of single-junction solar cells is somewhat insensitive to spectral irradiance. Adjusting the intensity of the simulator will compensate for spectral irradiance differences when compared to AM0 over the range of the spectral response of the cell. The adjustment produces a spectral irradiance that is larger than AM0 in some regions of the spectrum and smaller than AM0 in other regions of the spectrum. Following adjustment of the simulator intensity, cells may be characterized under “AM0” conditions. This method may be used as long as two conditions are met. First, it is necessary that the simulator is stable, meaning that spectral irradiance remains constant during the measurements on the standard cell and the cells to be characterized. Second, the voltage dependence of the spectral responses of the standard cell and cells to be characterized must be the same and not influenced by differences in the spectral irradiances of the solar simulator and AM0. The method requires stable standard cells for each of the types of single-junction cells to be characterized. Laboratory-based “AM0” characterization of single-junction solar cells has been carried out for many years with good results using this method.

The evolution of solar-cell technology for space applications has resulted in “state-of-the-art” cells with four and five junctions in series. Each junction is designed with a spectral response matched to one region of the spectral irradiance of AM0 in order to optimize the efficiency of solar cells. Figure 2 shows the structure of a multi-junction solar cell with four junctions. It is important to note that the four junctions are in series and that series nature of the cell requires that the steady-state current be the same in each of the junctions. The current in the solar cell operating at a given voltage is given by:

and (2)

(3)

where the variables in Equation 2 are the same as in Equation 1 except andare the lower and upper cut-off wavelength values, above and below which the spectral response is negligible and no longer contributes to cell current. The spectral response in Equation 2 characterizes the overall operation of the four junctions in optical absorption and carrier transport. However, the spectral responses and voltages in Equation 3, and respectively, are subscripted to show that they are different for each of the four junctions. The voltage across the cell is equal to the sum of the voltages across each of the four junctions, namely, . The wavelength ranges on each of the integrals, in the most general case, will overlap since it is not possible to fabricate materials with sharp wavelength cut-offs. Equation 3 shows the series nature of the current in multi-junction solar cells, namely, the current is the same in each of the junctions.

The sensitivity of a four-junction solar cell to spectral irradiance can be understood using Equation 3. Consider a cell that has been optimally designed for AM0 is to be characterized with a solar simulator. Assume the solar simulator has a spectral irradiance that is less than AM0 in the and wavelength range and the same as AM0 in the other three wavelength ranges shown in Equation 3. The lower spectral irradiance will result in less current in the junction optimized for the and wavelength range which in turn will limit the current in the cell due to the series nature of the four junctions. Equation 3 shows that the current reduction in the four junctions must be accomplished through changes in spectral responses of the other three junctions; this is the case because the spectral irradiances in the other three wavelength ranges are assumed to be the same as AM0. The collective interaction of the four junctions will result in redistribution of the cell voltage across the four junctions, which in turn changes the spectral responses of the four junctions and the cell current.

The role of the interaction of four junctions on the calibration errors of multi-junction solar cell, as compared to a single-junction cell, can be illustrated with an example. Assume the average spectral irradiance and the average spectral response are the same in the four wavelength regions in Equation 3. A one percent decrease in the spectral irradiance relative to AM0 over theand wavelength range will result in about a one percent decrease in the cell short-circuit current. A single-junction junction solar cell that responds in a similar fashion over the to wavelength range will experience only a 0.25 % decrease in short-circuit current. The reason is a one percent decrease in the integrated spectral irradiance over the and wavelength range in the multi-junction cell corresponds to a 0.25 % decrease in the integrated spectral irradiance over the to wavelength range in the single-junction cell.

A calibration procedure for multi-junction solar cells that uses a standard cell to set a solar simulator to “AM0” intensity may result in data that are not useful in optimizing the design of a test cell for space power generation. Assuming the voltage dependence of the spectral responses of each of the junctions in the standard and test cells are the same under the simulator “AM0” conditions, the junctions may be operating under conditions that are vastly different than AM0 conditions. It is possible that the test cell current-voltage characteristics measured under “AM0” conditions may not be useful in optimizing the cell design to improve efficiencies at the one percent level. Moreover, the complex nature of the interaction of the junctions does not lend itself to the use of an optical technique to compensate for the deficiencies in the “AM0” spectral irradiance.

The differences in the “AM0” and AM0 spectral irradiances are more problematic at the maximum power point than short-circuit conditions. The reason is the electrostatic potential barriers in each of the junctions are relatively small at the maximum power point as compared to short-circuit current conditions. Redistribution of voltages across the junctions can produce relatively large changes in the electrostatic potential barriers and produce major changes in the spectral responses of the junctions. Figure 3 shows the effect of forward bias on the quantum efficiency of a solar cell [1]. The solar cell is a triple-junction a-Si:H alloy-based thin-film solar cell that was illuminated with a solar simulator with an “AM0” spectral irradiance. The spectral irradiance was within one percent of AM0 in the wavelength range where the spectral response contributed to cell current. The figure shows the maximum quantum efficiency occurs at a wavelength of about 450 nm, serving as evidence that the top junction in this particular cell was limiting the current of the cell under short-circuit conditions. The maximum in the quantum efficiency shifted from 450 to 600 nm as the forward bias approached the maximum-power point showing that the middle and bottom junctions limited the cell current. The quantum efficiency of the cell changed markedly when the spectral irradiance of the simulator was altered [1]. A history of particle irradiation can also have a large effect on the dependence of the quantum efficiency of multi-junction cells under forward bias; this further complicates optimization of the design of cells used for space power generation in radiation environments.

It is clear that the voltage dependence of the spectral responses of multi-junction solar cells complicates optimization of cell design. While there are characterization methods that make it possible to use solar simulators in advancing the multi-junction solar cell technology, the series nature of the cells places more demands on the need for standard cells characterized under AM0 conditions. AM0 conditions are available only in space; near AM0 conditions can be achieved at altitudes in excess of 100,000 ft. The demand for greater access to AM0, and the costs associated with AM0 calibration, has generated interest in exploring lost-cost methods for AM0 solar cell calibration. The purposes of the Suntracker project is to calibrate cells in the stratosphere. The optical details of the project along with some calibration results will be discussed.

SUNTRACKER DESCRIPTION

The Suntracker is tethered below a balloon as it ascends through the tropopause and into the stratosphere. It is designed to point a solar cell at the sun and downlink data containing the cell short-circuit current, cell temperature, pressure, voltage reference and electronics module temperature. A diagram of the collimator and motor assemblies is shown in Figure 4. The two-axis tracker employs altitude and bearing motor assemblies that are controlled by an electronics module which serves to point

Figure 4. Diagram of collimator and motor assemblies.

the collimator at the sun. The collimator and electronics module together weigh less than thirteen ounces [2-4]. The collimator is a rectangular tube 4.00” long and 1.25” x 1.25” in area; the tube wall thickness is 0.062”. The aperture and cell areas are 1.00" x 1.00" and 0.79"x0.79", respectively. The design provides a plus or minus 1.5 ^o collimation of the full intensity of the sun on the solar cell. Since the intensity of the sun varies as the cosine of the incident angle, the dimensions of the collimator insure the intensity of the sun varies less than 0.04 % if the sun is tracked to plus or minus 1.5^o. The full-width at half maximum is plus or minus 6^o for the collimator. The dimensions of the collimator were selected to eliminate the contribution of light scattered from the balloon, earth, moon and clouds to the solar cell current. The solar cell is soldered to a copper plate that is mounted on the bottom of the collimator. A thermister is attached to the copper plate to measure the temperature of the solar cell. The collimator is painted with a flat black paint on the inside surfaces to minimize reflections of light. The exterior surfaces of the collimator, motors, motor bracket and support rod were also painted flat black to increase absorption of sunlight for heating the motor assemblies and solar cell and minimizing the effects of the low temperature environment at high altitudes.

SUNTRACKER OPTIC CHARACTERISTICS

The control of the Suntracker is accomplished with programmed microcontrollers that point the collimator at the sun during flights. It is necessary to understand the optical characteristics of the collimator in order to develope programs for the microcontrollers. The bearing and altitude motors shown in Figure 4 are actuated by electronics that use the cell current as a feedback signal. The system is designed to control the altitude and bearing motors in order to optimize the cell current. The altitude motor rotates the collimator in a plane vertical to the earth’s surface; the altitude angle ranges from 0^o, when the axis of the collimator is parallel to the earth’s surface, to 90^o when the collimator is perpendicular to the earth’s surface. The bearing motor rotates the collimator in a plane that is parallel to the earth’s surface; the bearing angle ranges between 0^o and 360^o. The optical characteristics can be understood by considering the manner in which the sun illuminates the solar cell as the collimator is rotated by the two motors. The sun overfills the solar cell when the collimator points directly at the sun. There is a range of bearing and altitude angles that result in the sun’s rays fully illuminating the solar cell since the collimator aperture area is larger than the cell area. Figure 5 shows the results of calculations of the normalized illumination of the cell for a number of altitude angles. For an altitude angle of 0^o, the normalized illumination remains constant to within 0.04 % for the bearing angle between 0^o, when the collimator is pointing at the sun, to plus or minus 1.5^o. For bearing angles greater than 1.5^o the cell is under filled and the normalized illumination decreases linearly until the bearing angle exceeds 12^o. No sunlight is incident on the cell for bearing angles greater than approximately 12^o. The figure shows that as the altitude angle increases, the overfilling of the cell extends to larger bearing angles. The decrease in the normalized illumination with increasing bearing angle is more gradual as the altitude angle increases. Figure 6 shows the calculated relationship between the bearing angle and the collimator-sun angle, namely, the angle subtended by the axis of the collimator and the suns rays. The slope of the collimator-sun angle curve decreases as the altitude angle increases until 90^o where the slope is zero and collimator-sun angle is independent of the bearing angle. The collimator optical characteristics for a constant bearing angle and variations in the altitude angle are the same as the 0^o altitude curve in Figure 5.

Outdoor measurements were carried out on a clear day to collect data in order to evaluate the results of the calculations. Figure 7 shows the dependence of the cell current expressed in the units of byte value (BV), the output signal of the electronics. The measurements were made when the solar altitude angle was about 70^o. The cell current remains approximately constant for bearing angles ranging between 0^o and about 3^o. The measurements are in good agreement with the calculated results. The calculated and measureed optical characteristics of the Suntracker were used to develop microcontroller programs for tracking the sun.

Apparatus was setup and outdoor measurements carried out to determine the ability of the Suntracker to track the sun. The Suntracker was placed on a variable-speed turntable and the tracking characteristics measured. The altitude and bearing motors were powered for a period time, referred to as pause 1. The motors coast for a period of time, pause 2, following pause 1 before coming to rest. The relationship between pause 1, pause 2 and the angular velocity of the turntable are listed in Table 1. For a 2 millisecond pause 1, the measurements show the angular velocity of the turntable may be increased from 4 to 9 degrees per second by decreasing pause 2 from 75 to 25 milliseconds. The angular velocity may be increased by increasing pause 1 to 3 milliseconds and using a 50 millisecond pause 2. Decreasing pause 2 to 25 milliseconds results in the collimator oscillating and poor tracking performance. The measurements were used to optimize the microcontroller programs.

SOLAR CELL CALIBRATION RESULTS

Seven flights have been attempted with five successful launches. Table 2 shows the launch dates and locations, burst altitudes, landing sites and balloon trajectory ranges. The scientific package was retrieved on the same day for the Suntracker I, III and IV flights. Hardware problems developed during the Suntracker VI and VII flights that resulted in the loss of GPS signals; the package was found within a few days of the launch by individuals and subsequently retrieved. A single-junction silicon solar cell was mounted in the collimator during the flights. The cell voltage data downlinked during the Suntracker IV and VI flights have been analyzed using Langley plots to determine the AM0 short-circuit current. The Suntracker VI uncorrected short-circuit current versus altitude is shown in Figure 8. Only the maximum currents were selected for use in the Langley plots. The cell current data illustrate the tracking characteristics during the ascent. For the most part the Suntracker was not locked on the sun during the flight. The video data showed the motors slowed down during the ascent as a result of the low atmospheric temperatures. Motor assemblies using lubricant with lower temperature specifications will be evaluated in future flights. Additionally, the stability of the scientific package and the collimator control algorithm will be investigated in order to improve the performance of the Suntracker system.

The cell temperature versus altitude during the Suntracker VI flight is shown in Figure 9. Also shown are the radiosonde data reported by the National Weather Service (NWS) on the day of the flight. The effect of solar heating on the cell current is apparent . While the solar cell temperature increased from –10 to about 0 ^oC as the balloon ascended from 80 to 96 kft, the atmospheric temperature remained at about –45 ^oC. The dependence of the cell and NWS temperatures in this altitude range suggests that the cell temperature may be higher at higher altitudes. If this is the case, it will be possible to operate cells closer to 25 ^oC at higher altitudes, and to determine the temperature coefficient of the short-circuit current as the package ascends.

Figure 10 is a Langley plot of the data for a single-junction silicon solar cell from the Suntracker IV and VI flights [5]. The optical air masses were calculated using Equation 11. The data have been corrected for the earth-sun distance and cell temperature, and fit with straight lines. The extrapolated AM0 short-circuit currents are 144.32 and 144.38 mA for the Suntracker IV and VI measurements, respectively. The average AM0 short-circuit current is 144.35 mA 0.02 %. The resolution of the eight-bit ADC in the Suntracker data acquisition system is 0.2 %, showing that the agreement between the two flights is better than the uncertainty in the measurements and probably reflects the statistics of the curve fitting etc. The AM0 short-circuit current of the single-junction silicon solar cell flown on the Suntracker flights was determined using the aircraft method at NASA Glenn Research Center [5]. The AM0 short-circuit current was 144.88 mA and within 0.36 % of the Suntracker average value. The results agree to within the statistics of the two methods, namely about 0.2 % for the Suntracker measurements and 0.6 % for the aircraft method.

CONCLUSIONS

The voltage dependence of the spectral responses of multi-junction solar cells complicates optimization of cell design. The series nature of multi-junction solar cells places more demands on the need for standard cells characterized under AM0 conditions. The AM0 short-circuit current of a single-junction silicon solar cell was determined using data collected during two Suntracker flights. The agreement in the two measurements was 0.02 %. The agreement in the AM0 short-circuit current of the cell measured with the Suntracker balloon method and NASA Glenn Research Center aircraft method was 0.36 %, which is within the uncertainty of the two methods.

REFERENCE

1. James R. Woodyard, “Laboratory Instrumentation and Techniques for Characterizing Multi-Junction Solar Cells,”Proceedings of the Twenty-Fifth Photovoltaic Specialists Conference, page 203, 1996.
2. Investigations to Characterize Multi-junction Solar Cells in the Stratosphere Using Low-Cost Balloon and Communication Technologies, Glenroy A. Bowe, Qianghua Wang, Richard R. Johnston, William J. Brown and James R. Woodyard, Sixteenth Space Photovoltaic Research and Technology Conference, 1999, NASA Conference Publication 2001-210747, page 189.
3. Investigations to Characterize Multi-junction Solar Cells in the Stratosphere Using Low-Cost Balloon and Communication Technologies, Glenroy A. Bowe, Qianghua Wang and James R. Woodyard, Twenty-Eight IEEE Photovoltaic Specialists Conference Proceedings, 2000, page 1328.
4. Report on Project to Characterize Multi-junction Solar Cells in the Stratosphere Using Low-Cost Balloon and Communication Technologies, Ali Mirza, David Sant, James R. Woodyard, Richard R. Johnston and William J. Brown, Seventeen Space Photovoltaic Research and Technology Conference, 2001, page 137.
5. High-Altitude Air Mass Zero Calibration of Solar Cells, James R. Woodyard and David B. Snyder, Eighteenth Space Photovoltaic Research and Technology Conference, 2003, in press.

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[1] This work was supported in part under NASA Grant NAG3-2801.