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Experimental tests of open-loop maximum-power-point tracking techniques for photovoltaic arrays
Solar Cells, 13 (1984) 185 - 195
185
EXPERIMENTAL TESTS OF OPEN-LOOP MAXIMUM-POWER-POINT TRACKING TECHNIQUES FOR PHOTOVOLTAIC ARRAYS G. W. HART Energy Laboratory, Massachusetts Institute o f Technology, Northeast Residential Experiment Station, 711 Virginia Road, Concord, MA 01742 (U.S.A.)
H. M. BRANZ and C. H. COX III Lincoln Laboratory, Massachusetts Institute o f Technology, P.O. Box 73, Lexington, MA 02173 (U.S.A.)
(Received March 12, 1984 ; accepted July 20, 1984)
Summary Two open-loop maximum-power-point tracking techniques for photovoltaic arrays are described and evaluated experimentally for the first time. These techniques both slave the operating point of a photovoltaic array to the state of a pilot cell. Experiments were performed to compare these open-loop methods with well-known array operating point control methods. For 25 days, array and pilot cell current-voltage data were recorded at 3 min intervals from a working photovoltaic string to compare the different tracking techniques. During this winter experimental period, minimal (about 1%) energy losses resulted from slaving the array voltage to a fixed multiple of the pilot cell open~ircuit voltage. Larger energy losses (about 7%) resulted from slaving the array current to a fixed multiple of the pilot cell short~ircuit current. At least 2.2% of the energy would be lost through array operation at a fixed voltage during this period. A m e t h o d of setting the multiplying factors which determine the details of the slaving algorithm is described. Because of its small energy losses, the voltage-slaved pilot cell m e t h o d is f o u n d to be a viable alternative for the control of photovoltaic arrays.
1. Introduction Maximum-power-point tracking o f photovoltaic arrays is usually achieved through control of the array operating voltage with feedback from the array power output. In this work we describe and evaluate two openloop pilot-cell-based methods for operating a photovoltaic array near its m a x i m u m power point. Open-loop tracking could reduce the complexity of the power conditioner and eliminate many of the problems encountered with conventional " h u n t i n g " maximum-power-point trackers (ref. 1, pp. 8 9 - 93). The voltage-slaved pilot cell m e t h o d is shown to be effective in 0379-6787/84/$3.00
© Elsevier Sequoia/Printed in The Netherlands
186
controlling photovoltaic arrays. Annual losses of only 0.8% - 1.2%, relative to ideal maximum-power-point tracking, can be expected from this technique. This compares favorably with other array control methods.
2. Pilot cell tracking Both the open-loop tracking methods evaluated in this study continuously control the photovoltaic array operating point on the basis of the o u t p u t of a pilot cell. A pilot cell is a photovoltaic unit of the same t ype as those in the array which it controls, but it is electrically separate from the array. The pilot cell can be as small as a single photovoltaic cell. An entire module could be used if it were the smallest available weather-sealed unit. The pilot cell tracking m e t hods which we investigated are achieved by slaving the array operating voltage to the pilot cell open-circuit voltage or by slaving the array operating cur r ent to the pilot cell short-circuit current. The array voltage or c ur r e nt is set to a fixed multiple of the pilot cell voltage or current respectively. These two pilot cell tracking methods were selected on the basis of four assumptions about pilot cells and arrays. As the irradiance and the cell temp er atu r e vary, near-constant ratios are maintained (1) between the open-circuit voltage of a pilot cell and that of the entire array, (2) between the open-circuit voltage of an array and the maximum-powerpoint voltage, (3) between the short-circuit current of a pilot cell module and that o f the entire array, and (4) between the short-circuit current of an array and the maximum-power-point current. If these four proportionalities hold, the pilot cell open-circuit voltage remains a constant fraction of the array maximum-power-point voltage, and the pilot cell short-circuit current remains a c ons t ant fraction of the array maximum-power-point current. Assumptions (1) and (3) are idealizations which are close to reality only if the pilot cell is identical bot h in kind and in placement with the cells which make up the array. For its electrical characteristics to mimic those o f the entire array, the pilot cell must be m o u n t e d in the same thermal environment as identical units in the array and positioned to intercept the same irradiance as the array. As a first-order approximation, the wiring resistance, diodes, leakage current and cell mismatch are ignored. Then the series-parallel connections in the array merely scale up the current-voltage (I-V) characteristics of the c o m p o n e n t units, and assumptions (1) and (3) are satisfied. However, small deviations from proport i onal i t y will be seen because a pilot cell which is short or open circuited delivers no pow er and therefore operates at a somewhat higher t em perat ure than the operating array. The energy which would have been delivered in electrical form appears instead as heat. The resulting t e m per a t ur e difference is no more than 5 10 °C and, because it varies consistently with irradiance, it should n o t much affect the pilot cell tracking.
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Fig. 1. I - V curves for varying cell t e m p e r a t u r e T (°C) at c o n s t a n t irradiance, demonstrating the limited variation in the current and voltage ratios (insolation, 100 mW cm -2 ): e, m a x i m u m p o w e r point. Fig. 2. I - V curves for varying irradiance L (roW cm -2) at c o n s t a n t temperature, demonstrating the limited variation in the current and voltage ratios (cell temperature, 30 °C): o, m a x i m u m p o w e r point.
Assumptions (2) and (4) approximate the behavior of typical photovoltaic arrays. Figures 1 and 2, adapted from ref. 2, indicate that an error of about +2% can be expected from each of these assumptions. These figures show a variety of I - V curves taken from a single photovoltaic module. The cell temperature is varied at constant irradiance in Fig. 1 and the irradiance is varied at constant cell temperature in Fig. 2. The ratio of the module maximum-power-point voltage to the open-circuit voltage is roughly constant. For this module it varies between 0.75 and 0.78 as the temperature varies over a 60 °C range. The ratio of the maximum-power-point current to the short-circuit current also remains roughly constant, ranging between 0.78 and 0.82, while the irradiance roughly doubles. These two examples show a limited number of cell temperature and irradiance conditions, but other published data [2] extend the approximate validity of assumptions (2) and (4) through the entire range of cell temperatures and irradiances likely to be encountered by terrestrial arrays. The theory outlined above predicts extremely small energy losses with either pilot cell tracking method. We expected, however, that factors n o t included in this simple theory would dominate the losses which occur
188
in an actual pilot-cell-controlled p h o t o v o l t a i c system. These factors include t e m p e r a t u r e effects, failures, soiling, shadowing and any o t h e r c o n d i t i o n which differentially affects the pilot cell and the main array, especially if the d i f f e r e n c e is a f u n c t i o n o f time. In o r d e r t o assess the pilot cell tracking m e t h o d s , an e x p e r i m e n t was t h e r e f o r e required.
3. E x p e r i m e n t a l details We r e p o r t on an e x p e r i m e n t designed t o e x a m i n e the effectiveness o f the t w o pilot cell strategies in controlling a string o f p h o t o v o l t a i c m o d u l e s for a 25 d a y p e r i o d o f w i n t e r o p e r a t i o n . C o m p l e t e I - V curves were r e c o r d e d f r o m a working p h o t o v o l t a i c array as p a r t o f the e x p e r i m e n t . The c o n t r o l l e d evaluation o f array o p e r a t i n g p o i n t c o n t r o l m e t h o d s requires I - V curve data. If c o m p l e t e I - V data were n o t available, t h e n the application o f any particular operating p o i n t c o n t r o l m e t h o d w o u l d m a k e it impossible to measure the results o f a n y o t h e r m e t h o d . A p h o t o v o l t a i c array operates at only one I - V p o i n t at any given time. By collecting entire I - V curves over time, we have available the i n f o r m a t i o n n e e d e d t o d e t e r m i n e w h a t w o u l d have h a p p e n e d u n d e r a n y o p e r a t i n g m e t h o d . A p h o t o v o l t a i c string I - V curve and collateral data were r e c o r d e d a u t o m a t i c a l l y every 3 min during the daylight h o u r s o f the entire test period. T h e string was d i s c o n n e c t e d f r o m the array by a relay f o r approxim a t e l y 1/2 s every 3 min while the I - V curve was swept using a capacitive load I - V curve t r a c e r [3]. This I - V curve t r a c e r t y p i c a l l y measures a curve in o n l y 20 ms, and so m o s t o f t h e 1/2 s p e r i o d was a l l o t t e d to relay switching. T h e quick sweep ensured an accurate I - V curve even u n d e r c o n d i t i o n s o f u n s t e a d y irradiance. F o r the r e m a i n d e r o f the 3 min interval the string was c o n n e c t e d , t o g e t h e r with the rest of the array, t o the system p o w e r cond i t i o n e r and delivered p o w e r as usual. Thus, the m e a s u r e d string m a i n t a i n e d the cell t e m p e r a t u r e o f an operating array. Had it been left o p e n or short circuited while I - V curve data were n o t being t a k e n , the string w o u l d have o p e r a t e d at a slightly higher t e m p e r a t u r e . The collateral data c o l l e c t e d every 3 min i n c l u d e d the pilot cell opencircuit voltages and short-circuit c u r r e n t . A m o d u l e o f the same t y p e as those in the array was rewired to a f f o r d electrical access to t h r e e pilot cells. T w o o f these p i l o t cells were individual p h o t o v o l t a i c cells. A third " p i l o t cell" consisted o f a string o f ten individual cells in series. The rewired m o d ule was t h e n installed in a blank space in t h e array racks. The open-circuit voltages o f one single cell and o f the ten-cell series string were m e a s u r e d directly. A voltage-zeroing circuit was used t o measure the short-circuit c u r r e n t o f t h e o t h e r pilot cell. T h e digitized I - V curves and pilot cell data were a u t o m a t i c a l l y transferred to magnetic tape. B e f o r e analysis, the I - V curve data were m a t h e matically s m o o t h e d t o eliminate systematic digitization errors (ref. 1, pp. 21 - 23).
189 We carried o u t t h e e x p e r i m e n t on a string f r o m t h e p r o t o t y p e s y s t e m at L i n c o l n L a b o r a t o r y , M a s s a c h u s e t t s I n s t i t u t e o f T e c h n o l o g y , N o r t h e a s t R e s i d e n t i a l E x p e r i m e n t S t a t i o n , C o n c o r d , MA [4]. This s t a n d - o f f m o u n t
Fig. 3. Prototype photovoltaic system, at Lincoln Laboratory, Massachusetts Institute of Technology, Northeast Residential Experiment Station, Concord, MA.
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4. Results
4.1. Voltage-slaved pilot cell m e t h o d The d.c. side of the power conditioner determines the operating poi nt o f the photovoltaic array. The voltage-slaved m e t h o d is realized with a circuit that continuously measures the open-circuit voltage of a pilot cell and sets the array voltage to a fixed multiple of the pilot cell voltage, according to V(array) = Cv V(pilot cell)
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where C~ is a dimensionless constant. The maximum-power-point voltage of an array is a bout 80% of the array open-circuit voltage for typical irradiances and cell temperatures. Thus the optimal value of Cv will be approximately 80% o f the num ber o f pilot cells that would be placed in series to duplicate the open-circuit voltage of the array. This value can be f o u n d in practice by varying Cv in the power conditioner circuitry while observing the array power and adjusting C~ until the o u t p u t power is maximized. Because most of the energy is delivered at times of high irradiance from the typical photovoltaic system, C~ is optimized if it is determined at a time of steady high irradiance. We envisage a " k n o b " on the power conditioner with which the hom e owner or system installer adjusts Cv while observing a po wer meter. This adjustment m e t h o d has this advantage: in the c o m m o n case o f array degradation resulting in two local power maxima (a " g l i t c h e d " I - V curve in the terminology of ref. 1), C~ can be adjusted so that the array voltage is at the larger of the two maxima. In these circumstances a conventional hunting maximum-power-point tracker might operate the system at a local m a x i m u m which is not the true m a xim um power point. To evaluate the voltage-slaved pilot cell m et hod, a c o m p u t e r program scanned through the I - V curve database and calculated the energy loss associated with this pilot cell m e t h o d for a range of C~. values. For each 3 min interval the software multiplied the pilot cell voltage by C, to find the array operating voltage and determined the string pow er o u t p u t at this voltage from the corresponding I - V curve. The total energy that would have been collected during the entire 25 day period under pilot cell control was then computed. The program followed the same procedure for each value of C, considered and also c o m p u t e d the total available energy (ideal maximum-power-point tracking) for these 25 days. The pilot cell energy o u t p u t with each value of Cv is c om par e d with the total available energy in Figs. 5 and 6.
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Fig. 5. Percentage loss of the available energy with the array voltage slaved to the single pilot cell as a function of the multiplier Cv. Figure 5 shows t h e results o f this e x p e r i m e n t f o r t h e single-cell pilot cell. T h e vertical axis represents the p e r c e n t a g e o f available energy lost with the array voltage slaved t o the single pilot cell. The h o r i z o n t a l axis represents t h e dimensionless multiplier Cv. T h e m i n i m u m loss occurs at Cv = 410, w h e r e o n l y 0.8% o f the available energy is sacrificed. This value o f C~ is a p p r o x i m a t e l y 80% o f the 504 cells in series in t h e m o n i t o r e d array, as e x p e c t e d . Figure 6 shows the results o f the same calculations f o r the p i l o t cell which consists o f t e n cells in series. T h e m i n i m u m here occurs at C~ = 41, w h e r e 1.2% o f the available energy is lost. During this p e r i o d the ten,cell pilot cell lost slightly m o r e e n e r g y t h a n did t h e single p i l o t cell. We do n o t c o n s i d e r t h a t t h e d i f f e r e n c e b e t w e e n energy losses o f 0.8% and 1.2% is significant e n o u g h t o indicate t h a t a one,cell pilot cell is superior t o a tencell p i l o t cell. T h e e x p e r i m e n t also s h o w e d t h a t t h e o p t i m u m value o f C~ will be easily d e t e r m i n e d in practice. We c a l c u l a t e d C~ f r o m the data r e c o r d e d closest to n o o n o n r a n d o m l y selected days w h e n t h e irradiance was above 0.5 kW m -2 and t h e r e was n o snow o n the array. This process is analogous t o c h o o s i n g a s u n n y d a y t o adjust the Cv k n o b on the p o w e r c o n d i t i o n e r and t u r n i n g t h e k n o b until t h e o u t p u t p o w e r is m a x i m i z e d . In all cases this p r o c e d u r e resulted in a value o f C~ b e t w e e n 405 and 415 f o r the single p i l o t cell and b e t w e e n 40.5 and 41.5 for the ten-cell p i l o t cell. These values are very near t h e o p t i m u m value o f C~ d e t e r m i n e d b y analyzing the entire 25 d a y period.
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A p o w e r c o n d i t i o n e r c o u l d also c o n t r o l the array operating p o i n t by regulating t h e array current. Once the p o w e r c o n d i t i o n e r selects an operating current, the array's I - V characteristic will determine the array operating voltage. The current-slaved m e t h o d is realized with a circuit that c o n t i n u ously measures the short-circuit current o f a pilot cell and sets the array current to a fixed multiple of the pilot cell current according to /(array) = CiI(pilot cell)
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where Ci is again a dimensionless constant. The m a x i m u m - p o w e r - p o i n t current of the string is a b o u t 90% o f the string short-circuit current. Thus the optimal C~ will be a p p r o x i m a t e l y 90% o f the n u m b e r of pilot cells that w o u l d be placed in parallel to equal the short-circuit current of the array. In order to evaluate the long-term energy loss with the current-slaved pilot cell m e t h o d , a c o m p u t e r performed calculations analogous to that described in Section 4.1. The energy o u t p u t that w o u l d have been realized with a current-slaved pilot cell tracker was compared with the total energy available to an ideal m a x i m u m - p o w e r - p o i n t tracker for a range of values of Ci. Figure 7 s h o w s the results of this experiment. The vertical axis represents the percentage o f available energy lost by the current-slaved m e t h o d . The horizontal axis represents the dimensionless multiplier Ci. The m i n i m u m energy loss occurs at Ci = 1.7, and with this multiplier 7.1% of the available energy is lost. This value of Ci is as e x p e c t e d , because the pilot cell is a single short-circuited cell, while the string from which the I - V curves were
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measured contained two cells in parallel. The large energy losses are most probably due to snow accumulations during the experimental period. If the pilot cell is partially covered with snow while the array is uncovered, or vice versa, the array operating current will be set incorrectly. This New England winter experimental period, which included several snowfalls, was therefore a worst-case test of the current-slaved method.
5. Conclusions This work indicates that the voltage-slaved pilot cell method is an effective operating point control technique for photovoltaic energy systems. I - V curves and pilot cell data were recorded from a working photovoltaic array every 3 rain over a 25 day winter experimental period. Voltage-multiplying array control is feasible because it results in the loss of 0.8%- 1.2% of the available energy for this period. A current-multiplying pilot cell method would result in the loss of 7.1% of the available energy during this period. The considerable superiority of voltage control over current control was a consequence of snow falling during the winter experimental period. When the irradiance to the array or the pilot cell is blocked by snow, the photovoltaic current falls linearly while the voltage falls only logarithmically. Thus, uneven array snow cover results in larger energy losses under current control than under voltage control. Because the experimental period did not include summer weather, the results cannot be considered to be representative of an entire year of
194 TABLE 1 Summary of the array control experiment, showing the total energy collected and the loss of available energy with various array operating point control methods Total energy
(kW h) Ideal maximum-power-point tracking Voltage multiplying (1 cell) Voltage multiplying (10 cells) Current multiplying (1 cell) Fixed voltage (best) Feedback-controlled maximum power tracking
Available energy losl (%)
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66.8 65.5 62.5 65.8 Model dependent
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o p e r a t i o n . A l t h o u g h we do n o t e x p e c t the y e a r l y e n e r g y losses to be greater t h a n t h e losses during this worst-case p e r i o d , we r e c o m m e n d e x t e n d i n g this e x p e r i m e n t t o w a r m e r snowless periods. It is possible t h a t seasonal fine t u n i n g o f t h e m u l t i p l y i n g c o n s t a n t c o n t r o l k n o b m i g h t slightly i m p r o v e the a n n u a l p e r f o r m a n c e in the p r e s e n c e o f wide seasonal t e m p e r a t u r e variations. It s h o u l d be r e m e m b e r e d t h a t a n y s h a d o w i n g , d i s t u r b a n c e or d a m a g e o f t h e p i l o t cell n o t a c c o m p a n i e d b y a resetting o f the m u l t i p l y i n g c o n s t a n t m i g h t r e d u c e t h e a r r a y e n e r g y o u t p u t with o p e n - l o o p tracking. T a b l e 1 s u m m a r i z e s t h e results of the e x p e r i m e n t a n d a f f o r d s a c o m p a r i s o n o f the p i l o t cell t e c h n i q u e s with c o n v e n t i o n a l a r r a y o p e r a t i n g p o i n t c o n t r o l m e t h o d s . T h e alternative o f fixed-voltage o p e r a t i o n o f this array w o u l d have resulted in e n e r g y losses o f at least 2.2% during this p e r i o d , a b o u t twice t h e losses o f the voltage-slaved m e t h o d . The various c o n v e n tional m a x i m u m - p o w e r - p o i n t t r a c k e r s t h a t are available c o m m e r c i a l l y w o u l d each result in d i f f e r e n t losses o f available energy, b u t each w o u l d c o n v e r t less of the available energy t h a n an ideal t r a c k e r . T h e r e f o r e t h e e n e r g y losses c o m p a r e d w i t h real m a x i m u m - p o w e r - p o i n t t r a c k e r s w o u l d be m o r e f a v o r a b l e t h a n T a b l e 1 indicates. On the basis o f the e x p e r i m e n t a l tests detailed in this p a p e r , o p e n - l o o p p i l o t cell t r a c k i n g can be c o n s i d e r e d to be a viable a l t e r n a t i v e f o r t h e c o n t r o l o f arrays.
Acknowledgments T h e a u t h o r s t h a n k H. F e n t o n , T. Warner, M. Buresch a n d M. Wong f o r their e x c e l l e n t help in design and c o n s t r u c t i o n o f the e x p e r i m e n t and its data a c q u i s i t i o n s y s t e m . We are also grateful t o L. C o w a n for her careful preparation of the manuscript. This w o r k was s p o n s o r e d by the U.S. D e p a r t m e n t of E n e r g y . T h e U.S. G o v e r n m e n t assumes n o r e s p o n s i b i l i t y f o r t h e i n f o r m a t i o n presented.
195 T h e p i l o t cell c o n c e p t was i n d e p e n d e n t l y d e v e l o p e d b y t h e a u t h o r s a t M a s s a c h u s e t t s I n s t i t u t e o f T e c h n o l o g y in J u l y 1 9 8 1 a n d b y A b a c u s C o n t r o l s Inc. o f S o m e r v i l l e , NJ. A b a c u s a t p r e s e n t has c o m m e r c i a l l y a v a i l a b l e p o w e r c o n d i t i o n e r s i n c o r p o r a t i n g t h e p i l o t cell t r a c k i n g t e c h n i q u e .
References 1 H. M. Branz, G. W. Hart and C. H. Cox, The photovoltaic array/power conditioner interface, Tech. Rep. DOE/ET/20279-170, October 1982 (U.S. Department of Energy; Lincoln Laboratory, Massachusetts Institute of Technology, Lexington, MA). 2 Solar Cell Array Design Handbook, Vol. 2 (JPL Publ. N77-14194), Jet Propulsion Laboratory, Pasadena, CA, 1976, pp. 3.2 - 3.5. 3 C. H. Cox and T. H. Warner, Swept measurement of high power I - V curves, Proc. 16th Photovoltaic Specialists' Conf., San Diego, CA, September 2 7 - 3 0 , 1982, IEEE, New York, 1982, pp. 1277 - 1283. 4 M. C. Russell, First year evaluation of prototype residential photovoltaic systems at the Northeast Residential Experiment Station, Tech. Rep. DOE/ET/20279-219, August 1982 (U.S. Department of Energy; Lincoln Laboratory, Massachusetts Institute of Technology, Lexington, MA).
185
EXPERIMENTAL TESTS OF OPEN-LOOP MAXIMUM-POWER-POINT TRACKING TECHNIQUES FOR PHOTOVOLTAIC ARRAYS G. W. HART Energy Laboratory, Massachusetts Institute o f Technology, Northeast Residential Experiment Station, 711 Virginia Road, Concord, MA 01742 (U.S.A.)
H. M. BRANZ and C. H. COX III Lincoln Laboratory, Massachusetts Institute o f Technology, P.O. Box 73, Lexington, MA 02173 (U.S.A.)
(Received March 12, 1984 ; accepted July 20, 1984)
Summary Two open-loop maximum-power-point tracking techniques for photovoltaic arrays are described and evaluated experimentally for the first time. These techniques both slave the operating point of a photovoltaic array to the state of a pilot cell. Experiments were performed to compare these open-loop methods with well-known array operating point control methods. For 25 days, array and pilot cell current-voltage data were recorded at 3 min intervals from a working photovoltaic string to compare the different tracking techniques. During this winter experimental period, minimal (about 1%) energy losses resulted from slaving the array voltage to a fixed multiple of the pilot cell open~ircuit voltage. Larger energy losses (about 7%) resulted from slaving the array current to a fixed multiple of the pilot cell short~ircuit current. At least 2.2% of the energy would be lost through array operation at a fixed voltage during this period. A m e t h o d of setting the multiplying factors which determine the details of the slaving algorithm is described. Because of its small energy losses, the voltage-slaved pilot cell m e t h o d is f o u n d to be a viable alternative for the control of photovoltaic arrays.
1. Introduction Maximum-power-point tracking o f photovoltaic arrays is usually achieved through control of the array operating voltage with feedback from the array power output. In this work we describe and evaluate two openloop pilot-cell-based methods for operating a photovoltaic array near its m a x i m u m power point. Open-loop tracking could reduce the complexity of the power conditioner and eliminate many of the problems encountered with conventional " h u n t i n g " maximum-power-point trackers (ref. 1, pp. 8 9 - 93). The voltage-slaved pilot cell m e t h o d is shown to be effective in 0379-6787/84/$3.00
© Elsevier Sequoia/Printed in The Netherlands
186
controlling photovoltaic arrays. Annual losses of only 0.8% - 1.2%, relative to ideal maximum-power-point tracking, can be expected from this technique. This compares favorably with other array control methods.
2. Pilot cell tracking Both the open-loop tracking methods evaluated in this study continuously control the photovoltaic array operating point on the basis of the o u t p u t of a pilot cell. A pilot cell is a photovoltaic unit of the same t ype as those in the array which it controls, but it is electrically separate from the array. The pilot cell can be as small as a single photovoltaic cell. An entire module could be used if it were the smallest available weather-sealed unit. The pilot cell tracking m e t hods which we investigated are achieved by slaving the array operating voltage to the pilot cell open-circuit voltage or by slaving the array operating cur r ent to the pilot cell short-circuit current. The array voltage or c ur r e nt is set to a fixed multiple of the pilot cell voltage or current respectively. These two pilot cell tracking methods were selected on the basis of four assumptions about pilot cells and arrays. As the irradiance and the cell temp er atu r e vary, near-constant ratios are maintained (1) between the open-circuit voltage of a pilot cell and that of the entire array, (2) between the open-circuit voltage of an array and the maximum-powerpoint voltage, (3) between the short-circuit current of a pilot cell module and that o f the entire array, and (4) between the short-circuit current of an array and the maximum-power-point current. If these four proportionalities hold, the pilot cell open-circuit voltage remains a constant fraction of the array maximum-power-point voltage, and the pilot cell short-circuit current remains a c ons t ant fraction of the array maximum-power-point current. Assumptions (1) and (3) are idealizations which are close to reality only if the pilot cell is identical bot h in kind and in placement with the cells which make up the array. For its electrical characteristics to mimic those o f the entire array, the pilot cell must be m o u n t e d in the same thermal environment as identical units in the array and positioned to intercept the same irradiance as the array. As a first-order approximation, the wiring resistance, diodes, leakage current and cell mismatch are ignored. Then the series-parallel connections in the array merely scale up the current-voltage (I-V) characteristics of the c o m p o n e n t units, and assumptions (1) and (3) are satisfied. However, small deviations from proport i onal i t y will be seen because a pilot cell which is short or open circuited delivers no pow er and therefore operates at a somewhat higher t em perat ure than the operating array. The energy which would have been delivered in electrical form appears instead as heat. The resulting t e m per a t ur e difference is no more than 5 10 °C and, because it varies consistently with irradiance, it should n o t much affect the pilot cell tracking.
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Assumptions (2) and (4) approximate the behavior of typical photovoltaic arrays. Figures 1 and 2, adapted from ref. 2, indicate that an error of about +2% can be expected from each of these assumptions. These figures show a variety of I - V curves taken from a single photovoltaic module. The cell temperature is varied at constant irradiance in Fig. 1 and the irradiance is varied at constant cell temperature in Fig. 2. The ratio of the module maximum-power-point voltage to the open-circuit voltage is roughly constant. For this module it varies between 0.75 and 0.78 as the temperature varies over a 60 °C range. The ratio of the maximum-power-point current to the short-circuit current also remains roughly constant, ranging between 0.78 and 0.82, while the irradiance roughly doubles. These two examples show a limited number of cell temperature and irradiance conditions, but other published data [2] extend the approximate validity of assumptions (2) and (4) through the entire range of cell temperatures and irradiances likely to be encountered by terrestrial arrays. The theory outlined above predicts extremely small energy losses with either pilot cell tracking method. We expected, however, that factors n o t included in this simple theory would dominate the losses which occur
188
in an actual pilot-cell-controlled p h o t o v o l t a i c system. These factors include t e m p e r a t u r e effects, failures, soiling, shadowing and any o t h e r c o n d i t i o n which differentially affects the pilot cell and the main array, especially if the d i f f e r e n c e is a f u n c t i o n o f time. In o r d e r t o assess the pilot cell tracking m e t h o d s , an e x p e r i m e n t was t h e r e f o r e required.
3. E x p e r i m e n t a l details We r e p o r t on an e x p e r i m e n t designed t o e x a m i n e the effectiveness o f the t w o pilot cell strategies in controlling a string o f p h o t o v o l t a i c m o d u l e s for a 25 d a y p e r i o d o f w i n t e r o p e r a t i o n . C o m p l e t e I - V curves were r e c o r d e d f r o m a working p h o t o v o l t a i c array as p a r t o f the e x p e r i m e n t . The c o n t r o l l e d evaluation o f array o p e r a t i n g p o i n t c o n t r o l m e t h o d s requires I - V curve data. If c o m p l e t e I - V data were n o t available, t h e n the application o f any particular operating p o i n t c o n t r o l m e t h o d w o u l d m a k e it impossible to measure the results o f a n y o t h e r m e t h o d . A p h o t o v o l t a i c array operates at only one I - V p o i n t at any given time. By collecting entire I - V curves over time, we have available the i n f o r m a t i o n n e e d e d t o d e t e r m i n e w h a t w o u l d have h a p p e n e d u n d e r a n y o p e r a t i n g m e t h o d . A p h o t o v o l t a i c string I - V curve and collateral data were r e c o r d e d a u t o m a t i c a l l y every 3 min during the daylight h o u r s o f the entire test period. T h e string was d i s c o n n e c t e d f r o m the array by a relay f o r approxim a t e l y 1/2 s every 3 min while the I - V curve was swept using a capacitive load I - V curve t r a c e r [3]. This I - V curve t r a c e r t y p i c a l l y measures a curve in o n l y 20 ms, and so m o s t o f t h e 1/2 s p e r i o d was a l l o t t e d to relay switching. T h e quick sweep ensured an accurate I - V curve even u n d e r c o n d i t i o n s o f u n s t e a d y irradiance. F o r the r e m a i n d e r o f the 3 min interval the string was c o n n e c t e d , t o g e t h e r with the rest of the array, t o the system p o w e r cond i t i o n e r and delivered p o w e r as usual. Thus, the m e a s u r e d string m a i n t a i n e d the cell t e m p e r a t u r e o f an operating array. Had it been left o p e n or short circuited while I - V curve data were n o t being t a k e n , the string w o u l d have o p e r a t e d at a slightly higher t e m p e r a t u r e . The collateral data c o l l e c t e d every 3 min i n c l u d e d the pilot cell opencircuit voltages and short-circuit c u r r e n t . A m o d u l e o f the same t y p e as those in the array was rewired to a f f o r d electrical access to t h r e e pilot cells. T w o o f these p i l o t cells were individual p h o t o v o l t a i c cells. A third " p i l o t cell" consisted o f a string o f ten individual cells in series. The rewired m o d ule was t h e n installed in a blank space in t h e array racks. The open-circuit voltages o f one single cell and o f the ten-cell series string were m e a s u r e d directly. A voltage-zeroing circuit was used t o measure the short-circuit c u r r e n t o f t h e o t h e r pilot cell. T h e digitized I - V curves and pilot cell data were a u t o m a t i c a l l y transferred to magnetic tape. B e f o r e analysis, the I - V curve data were m a t h e matically s m o o t h e d t o eliminate systematic digitization errors (ref. 1, pp. 21 - 23).
189 We carried o u t t h e e x p e r i m e n t on a string f r o m t h e p r o t o t y p e s y s t e m at L i n c o l n L a b o r a t o r y , M a s s a c h u s e t t s I n s t i t u t e o f T e c h n o l o g y , N o r t h e a s t R e s i d e n t i a l E x p e r i m e n t S t a t i o n , C o n c o r d , MA [4]. This s t a n d - o f f m o u n t
Fig. 3. Prototype photovoltaic system, at Lincoln Laboratory, Massachusetts Institute of Technology, Northeast Residential Experiment Station, Concord, MA.
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4. Results
4.1. Voltage-slaved pilot cell m e t h o d The d.c. side of the power conditioner determines the operating poi nt o f the photovoltaic array. The voltage-slaved m e t h o d is realized with a circuit that continuously measures the open-circuit voltage of a pilot cell and sets the array voltage to a fixed multiple of the pilot cell voltage, according to V(array) = Cv V(pilot cell)
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where C~ is a dimensionless constant. The maximum-power-point voltage of an array is a bout 80% of the array open-circuit voltage for typical irradiances and cell temperatures. Thus the optimal value of Cv will be approximately 80% o f the num ber o f pilot cells that would be placed in series to duplicate the open-circuit voltage of the array. This value can be f o u n d in practice by varying Cv in the power conditioner circuitry while observing the array power and adjusting C~ until the o u t p u t power is maximized. Because most of the energy is delivered at times of high irradiance from the typical photovoltaic system, C~ is optimized if it is determined at a time of steady high irradiance. We envisage a " k n o b " on the power conditioner with which the hom e owner or system installer adjusts Cv while observing a po wer meter. This adjustment m e t h o d has this advantage: in the c o m m o n case o f array degradation resulting in two local power maxima (a " g l i t c h e d " I - V curve in the terminology of ref. 1), C~ can be adjusted so that the array voltage is at the larger of the two maxima. In these circumstances a conventional hunting maximum-power-point tracker might operate the system at a local m a x i m u m which is not the true m a xim um power point. To evaluate the voltage-slaved pilot cell m et hod, a c o m p u t e r program scanned through the I - V curve database and calculated the energy loss associated with this pilot cell m e t h o d for a range of C~. values. For each 3 min interval the software multiplied the pilot cell voltage by C, to find the array operating voltage and determined the string pow er o u t p u t at this voltage from the corresponding I - V curve. The total energy that would have been collected during the entire 25 day period under pilot cell control was then computed. The program followed the same procedure for each value of C, considered and also c o m p u t e d the total available energy (ideal maximum-power-point tracking) for these 25 days. The pilot cell energy o u t p u t with each value of Cv is c om par e d with the total available energy in Figs. 5 and 6.
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Fig. 5. Percentage loss of the available energy with the array voltage slaved to the single pilot cell as a function of the multiplier Cv. Figure 5 shows t h e results o f this e x p e r i m e n t f o r t h e single-cell pilot cell. T h e vertical axis represents the p e r c e n t a g e o f available energy lost with the array voltage slaved t o the single pilot cell. The h o r i z o n t a l axis represents t h e dimensionless multiplier Cv. T h e m i n i m u m loss occurs at Cv = 410, w h e r e o n l y 0.8% o f the available energy is sacrificed. This value o f C~ is a p p r o x i m a t e l y 80% o f the 504 cells in series in t h e m o n i t o r e d array, as e x p e c t e d . Figure 6 shows the results o f the same calculations f o r the p i l o t cell which consists o f t e n cells in series. T h e m i n i m u m here occurs at C~ = 41, w h e r e 1.2% o f the available energy is lost. During this p e r i o d the ten,cell pilot cell lost slightly m o r e e n e r g y t h a n did t h e single p i l o t cell. We do n o t c o n s i d e r t h a t t h e d i f f e r e n c e b e t w e e n energy losses o f 0.8% and 1.2% is significant e n o u g h t o indicate t h a t a one,cell pilot cell is superior t o a tencell p i l o t cell. T h e e x p e r i m e n t also s h o w e d t h a t t h e o p t i m u m value o f C~ will be easily d e t e r m i n e d in practice. We c a l c u l a t e d C~ f r o m the data r e c o r d e d closest to n o o n o n r a n d o m l y selected days w h e n t h e irradiance was above 0.5 kW m -2 and t h e r e was n o snow o n the array. This process is analogous t o c h o o s i n g a s u n n y d a y t o adjust the Cv k n o b on the p o w e r c o n d i t i o n e r and t u r n i n g t h e k n o b until t h e o u t p u t p o w e r is m a x i m i z e d . In all cases this p r o c e d u r e resulted in a value o f C~ b e t w e e n 405 and 415 f o r the single p i l o t cell and b e t w e e n 40.5 and 41.5 for the ten-cell p i l o t cell. These values are very near t h e o p t i m u m value o f C~ d e t e r m i n e d b y analyzing the entire 25 d a y period.
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A p o w e r c o n d i t i o n e r c o u l d also c o n t r o l the array operating p o i n t by regulating t h e array current. Once the p o w e r c o n d i t i o n e r selects an operating current, the array's I - V characteristic will determine the array operating voltage. The current-slaved m e t h o d is realized with a circuit that c o n t i n u ously measures the short-circuit current o f a pilot cell and sets the array current to a fixed multiple of the pilot cell current according to /(array) = CiI(pilot cell)
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where Ci is again a dimensionless constant. The m a x i m u m - p o w e r - p o i n t current of the string is a b o u t 90% o f the string short-circuit current. Thus the optimal C~ will be a p p r o x i m a t e l y 90% o f the n u m b e r of pilot cells that w o u l d be placed in parallel to equal the short-circuit current of the array. In order to evaluate the long-term energy loss with the current-slaved pilot cell m e t h o d , a c o m p u t e r performed calculations analogous to that described in Section 4.1. The energy o u t p u t that w o u l d have been realized with a current-slaved pilot cell tracker was compared with the total energy available to an ideal m a x i m u m - p o w e r - p o i n t tracker for a range of values of Ci. Figure 7 s h o w s the results of this experiment. The vertical axis represents the percentage o f available energy lost by the current-slaved m e t h o d . The horizontal axis represents the dimensionless multiplier Ci. The m i n i m u m energy loss occurs at Ci = 1.7, and with this multiplier 7.1% of the available energy is lost. This value of Ci is as e x p e c t e d , because the pilot cell is a single short-circuited cell, while the string from which the I - V curves were
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measured contained two cells in parallel. The large energy losses are most probably due to snow accumulations during the experimental period. If the pilot cell is partially covered with snow while the array is uncovered, or vice versa, the array operating current will be set incorrectly. This New England winter experimental period, which included several snowfalls, was therefore a worst-case test of the current-slaved method.
5. Conclusions This work indicates that the voltage-slaved pilot cell method is an effective operating point control technique for photovoltaic energy systems. I - V curves and pilot cell data were recorded from a working photovoltaic array every 3 rain over a 25 day winter experimental period. Voltage-multiplying array control is feasible because it results in the loss of 0.8%- 1.2% of the available energy for this period. A current-multiplying pilot cell method would result in the loss of 7.1% of the available energy during this period. The considerable superiority of voltage control over current control was a consequence of snow falling during the winter experimental period. When the irradiance to the array or the pilot cell is blocked by snow, the photovoltaic current falls linearly while the voltage falls only logarithmically. Thus, uneven array snow cover results in larger energy losses under current control than under voltage control. Because the experimental period did not include summer weather, the results cannot be considered to be representative of an entire year of
194 TABLE 1 Summary of the array control experiment, showing the total energy collected and the loss of available energy with various array operating point control methods Total energy
(kW h) Ideal maximum-power-point tracking Voltage multiplying (1 cell) Voltage multiplying (10 cells) Current multiplying (1 cell) Fixed voltage (best) Feedback-controlled maximum power tracking
Available energy losl (%)
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o p e r a t i o n . A l t h o u g h we do n o t e x p e c t the y e a r l y e n e r g y losses to be greater t h a n t h e losses during this worst-case p e r i o d , we r e c o m m e n d e x t e n d i n g this e x p e r i m e n t t o w a r m e r snowless periods. It is possible t h a t seasonal fine t u n i n g o f t h e m u l t i p l y i n g c o n s t a n t c o n t r o l k n o b m i g h t slightly i m p r o v e the a n n u a l p e r f o r m a n c e in the p r e s e n c e o f wide seasonal t e m p e r a t u r e variations. It s h o u l d be r e m e m b e r e d t h a t a n y s h a d o w i n g , d i s t u r b a n c e or d a m a g e o f t h e p i l o t cell n o t a c c o m p a n i e d b y a resetting o f the m u l t i p l y i n g c o n s t a n t m i g h t r e d u c e t h e a r r a y e n e r g y o u t p u t with o p e n - l o o p tracking. T a b l e 1 s u m m a r i z e s t h e results of the e x p e r i m e n t a n d a f f o r d s a c o m p a r i s o n o f the p i l o t cell t e c h n i q u e s with c o n v e n t i o n a l a r r a y o p e r a t i n g p o i n t c o n t r o l m e t h o d s . T h e alternative o f fixed-voltage o p e r a t i o n o f this array w o u l d have resulted in e n e r g y losses o f at least 2.2% during this p e r i o d , a b o u t twice t h e losses o f the voltage-slaved m e t h o d . The various c o n v e n tional m a x i m u m - p o w e r - p o i n t t r a c k e r s t h a t are available c o m m e r c i a l l y w o u l d each result in d i f f e r e n t losses o f available energy, b u t each w o u l d c o n v e r t less of the available energy t h a n an ideal t r a c k e r . T h e r e f o r e t h e e n e r g y losses c o m p a r e d w i t h real m a x i m u m - p o w e r - p o i n t t r a c k e r s w o u l d be m o r e f a v o r a b l e t h a n T a b l e 1 indicates. On the basis o f the e x p e r i m e n t a l tests detailed in this p a p e r , o p e n - l o o p p i l o t cell t r a c k i n g can be c o n s i d e r e d to be a viable a l t e r n a t i v e f o r t h e c o n t r o l o f arrays.
Acknowledgments T h e a u t h o r s t h a n k H. F e n t o n , T. Warner, M. Buresch a n d M. Wong f o r their e x c e l l e n t help in design and c o n s t r u c t i o n o f the e x p e r i m e n t and its data a c q u i s i t i o n s y s t e m . We are also grateful t o L. C o w a n for her careful preparation of the manuscript. This w o r k was s p o n s o r e d by the U.S. D e p a r t m e n t of E n e r g y . T h e U.S. G o v e r n m e n t assumes n o r e s p o n s i b i l i t y f o r t h e i n f o r m a t i o n presented.
195 T h e p i l o t cell c o n c e p t was i n d e p e n d e n t l y d e v e l o p e d b y t h e a u t h o r s a t M a s s a c h u s e t t s I n s t i t u t e o f T e c h n o l o g y in J u l y 1 9 8 1 a n d b y A b a c u s C o n t r o l s Inc. o f S o m e r v i l l e , NJ. A b a c u s a t p r e s e n t has c o m m e r c i a l l y a v a i l a b l e p o w e r c o n d i t i o n e r s i n c o r p o r a t i n g t h e p i l o t cell t r a c k i n g t e c h n i q u e .
References 1 H. M. Branz, G. W. Hart and C. H. Cox, The photovoltaic array/power conditioner interface, Tech. Rep. DOE/ET/20279-170, October 1982 (U.S. Department of Energy; Lincoln Laboratory, Massachusetts Institute of Technology, Lexington, MA). 2 Solar Cell Array Design Handbook, Vol. 2 (JPL Publ. N77-14194), Jet Propulsion Laboratory, Pasadena, CA, 1976, pp. 3.2 - 3.5. 3 C. H. Cox and T. H. Warner, Swept measurement of high power I - V curves, Proc. 16th Photovoltaic Specialists' Conf., San Diego, CA, September 2 7 - 3 0 , 1982, IEEE, New York, 1982, pp. 1277 - 1283. 4 M. C. Russell, First year evaluation of prototype residential photovoltaic systems at the Northeast Residential Experiment Station, Tech. Rep. DOE/ET/20279-219, August 1982 (U.S. Department of Energy; Lincoln Laboratory, Massachusetts Institute of Technology, Lexington, MA).