- Email: [email protected]
Microcomputer-controlled simulator of a photovoltaic generator using a programmable voltage generator
Solar Cells, 17 (1986) 383-390
383
M I C R O C O M P U T E R - C O N T R O L L E D S I M U L A T O R OF A PHOTOVOLTAIC G E N E R A T O R USING A P R O G R A M M A B L E VOLTAGE GENERATOR
T. E A S W A R A K H A N T H A N ,
J. BOTTIN, A. EL-SLASSI. R and S. R A V E L E T
Institut des Sciences de l'IngJnieur, Laboratoire d'Electronique et de Physique des Interfaces, UniversitJ de Nancy, Parc Robert Bentz, 54500 Vandoeuvre l$s Nancy
(France) (Received February 4, 1985; accepted July 16, 1985)
Summary A microcomputer-controlled simulator incorporating a programmable d.c. voltage generator, a programmable multimeter, and a power amplifier for physically simulating the power characteristics of solar photovoltaic generators based on a theoretical model are presented. Under software control in real time, with a linear interpolating iterative technique, the operating points of a photovoltaic generator-load system are established with sufficient accuracy. The main feature o f the simulator is its flexibility, since the influence of insolation, temperature and various array parameters on the array o u t p u t characteristics can be readily simulated. Physical simulations of a given photovoltaic generator with a variable resistance and a motor-pump load, direct-coupled and with an adaptor, are presented as examples.
1. Introduction The fact that photovoltaic (PV) generators respond differently than conventional ones necessitates a detailed study of would-be PV systems. Although the software programs [1,2] in which all system components are theoretically modelled simulate the performance of PV systems, the theoretical techniques must be validated through experimentation with such system sub-components as power conditioners. More often than not, in the absence of solar modules, it is necessary in an experimental study to use simulators which physically act as PV generators. In terms of reliability and convenience, greater control of a scheduled laboratory experiment is possible with a simulator than with natural sunlight. The methods generally used to devise such simulators [3,4] are the following: modifying a voltage source so that its internal resistance varies exponentially with current; amplifying the current and voltage of a solar 0379-6787/86/$3130
© Elsevier Sequoia/Printed in The Netherlands
384 cell; forming the PV generator equivalent circuit by using a constant current source and a diode-resistor network. Although such simulators have their merits, their limited flexibility in readily simulating the influence of insolation, temperature and various array parameters is an inconvenience that must be noted. Furthermore, there are potential problems of stability and linearity caused by the closed-loop electronic circuits. In this paper we introduce a solar-array simulator based on a Commodore CBM-4016 microcomputer with an Adret d.c. voltage generator, a Keithley multimeter (both programmable), and a power amplifier. A schematic diagram of the system is presented in Fig. 1. The operating points are approached for the changes in load, insolation and temperature, and also in various array parameters using a linear-interpolation iterative technique. In brief, the computer calculates successively the current and voltage at the intersection of the PV generator I - V c u r v e and a straight line through two points subsequently processed on the load-operating curve. It then programs the d.c. generator to apply the computed voltage across the load, reads the resulting current measured by the multimeter at its IEEE port, and tests the relative difference between the c o m p u t e d and measured currents. The program enters a waiting loop once the desired relative difference is attained. The extended flexibility is shown, n o t only by the elimination of closed-loop electronic circuits, but also by the possibility of simulating the influences of load, insolation and temperature by feeding them into the microcomputer through its i n p u t / o u t p u t ports or the keyboard. Moreover, the computer enables the characteristics of any type of solar panel to be reproduced once their parameters are known.
2. Model
o f the P V g e n e r a t o r
The current-voltage relation of a PV generator with Np parallel strings each comprising N s solar cells, with a one-diode equivalent electrical
AIO~
ompiifierLoad
.
I I
4
I I
User
?
i
L_
IEEE Port CBM-4016
Fig. 1. Schematic diagram of the simulator.
f TV
385
circuit assumed, is given by
I=Nplph--NploFexp~BIV+IRs~
(1)
where I and V are respectively the current and voltage at the o u t p u t of the PV generator, B -1 is the thermal voltage, and Rs is the series resistance of a solar cell [5]. The model assumes a negligible shunt conductance and the use o f identical cells operating under the same environmental conditions. The photocurrent Iph is a function of illumination ~b(W m -2) and temperature T. When only moderate temperatures (below 75 °C) and illuminations under 1000 W m -2 are considered, Iph may be written as Iph = C~(1 +
fJT)~S
(2)
where S is the area of a solar cell [6]. The constants ~ and ~ can be found in the experimental data or in the manufacturer's data for a solar panel. The saturation current I0 is only a function of temperature. It may be written [5, 7] as
Io = CmST3 exp(" E'°~ kT/
(3)
where Ego is the energy gap of the device material at 0 K, and k and Cm are the Boltzmann constant and the device specific constant respectively [5, 7]. It is assumed that Cm is independent of temperature.
3. Ascertaining the operating point Figure 2 shows the I-V curve of a solar array at a given temperature T, illumination ~ and load curve AB. The operating point P moves along the I-V curve between the open-circuit voltage Voc and the short-circuit current
~T
o
/B
vI
vz Vo~ ~v
Fig. 2. Principle of convergence from an initial point A to the operating point P through P0, P1 . . . . . P. The arrow indicates the converging direction.
386 Isc as the load varies. In order to ascertain the operating point the computer executes a BASIC program in real time. The main steps are outlined below. 3.1. Step 1: initialization
Once the computer calculates Voc, Isc, Iph and Io from the input physical variables and the array parameters, it programs the d.c. generator to apply a starting voltage VI (initially guessed to be about 0.25Voc) across the load and reads the resulting current It,1 at its IEEE port (see Fig. 2), measured and sent by the multimeter. If Ira1 is smaller than some predetermined lower limit relative to Isc, this step is repeated with a starting value of 0.5( V1 ÷ Voc). If I ~ 1 is relatively larger compared with Isc , the starting value is reduced to
0.5v . 3.2. Step 2: co m put at i on and testing
The c o m p u t e r calculates the current Icl and voltage V2 at the intersection P0 of the I - V curve and the straight line that runs through the origin and (V l, Im 1)- The generator then outputs V2 and the computer reads the current Ira2 through the load. The c o m p u t e r now tests the relative difference between the current measured Ira2 and c o m p u t e d Icl. If this difference is greater than 1%, the program repeats Step 2, this time computing the current and voltage at the intersection P1 of the array I - V curve and the straight line that runs through the last consecutively measured points on the load curve (V1, Im 1 ), (V2, Im: ). The straight line is represented by I = mV + c
(4)
where m and c are determined from the measured values, and c is zero for the very first iteration. The elimination o f V from eqns. (4) and (1) leads to the following nonlinear equation: I = N p I p h --NpI0(ex p [ S ( I ( 1 / m N s + Rs/Np) -- c/mNs} ] --1)
(5)
The program utilizes the second-order N e w t o n - R a p h s o n iterative technique to solve this equation, for which it deduces a suitable initial value. Once the current is determined, the voltage is computed from eqn. (4). With this approach the load curve is constantly traced and the convergence to the operating point is accelerated. In Fig. 2 only two such linear interpolating iterations are indicated. 3.3. Step 3: convergence when load changes
If the relative difference is less than 1%, which is defined as the criterion for the convergence to the operating point, the program enters and waits in a closed loop in which the computer constantly reads the current at its IEEE port and tests the relative difference. Whenever there is a variation in load such that the 1% limit is exceeded the program returns to Step 2; the iterations are repeated until the new operating point is reached. Figure 3 illustrates the convergence from P to the new operating point Q
387
I
[so 0++ Im]
....... :-----_-_---~
iml
.......................
ICl
Iml 7 Vl
V2 Voc
~V
e"
V2
v 1 vo~, Vo~ v
Fig. 3. Convergence f r o m P to the operating p o i n t Q through P0, PI, • • •, Q w h e n the load curve shifts f r o m AB to A ' B ' . Fig. 4. Convergence f r o m P to the operating p o i n t R through P0, P1 . . . . . illumination changes f r o m ¢ to ¢1.
R w h e n the
when the load-operating curve shifts from AB to A'B', indicating only two linear interpolating iterations.
3.4. Step 4: variations in illumination and temperature While waiting in the loop the program also enters the k e y b o a r d when the BASIC instruction GET is used. The keyboard loop allows the user to enter new values for temperature or illumination or both. For example, if a new illumination value ¢I is entered, the computer calculates Vocl, Iscl, Iphl and I01 anew and returns to Step 2. The iteration process continues until the computer arrives at the new operating point R with the desired relative difference. The program then enters the waiting loop where the microc o m p u t e r looks for the next alteration. Figure 4 illustrates the convergence with t w o such iterations for variation in illumination. 4. Remarks on system components
4.1. Programmable devices The C o m m o d o r e CBM-4016 microcomputer acts as the controller, and addresses and programs the Adret-103A d.c. voltage-current standard in its autoranging voltage m o d e by sending alphanumeric strings via the IEEE-488 bus. In the same manner it activates the programmable Keithley-195 with standard IEEE-488 interface to operate as a d.c. autoranging voltmeter with the desired reading rate. The multimeter could also be used as an ammeter to measure the current through the load directly. Instead, the current is determined from a measurement of the voltage across a k n o w n small shunt resistance. This avoids possibly erroneous reading resulting from the variation in internal resistance when the range of measurement in the current measuring m o d e changes automatically. The non-IEEE device used is the Watanabe plotter which is addressed and programmed through the user
388 port of CBM. It plots the operating current against voltage every time there is convergence to the operating point as a result of an alteration and thus allows the visualization of the I - V characteristics.
4.2. Power amplifier The Adret d.c. generator is limited in current to a maximum value of 110 mA. In order to simulate the solar panels which have important shortcircuit currents, a d.c. power amplifier is designed with the maximum output voltage and current (50 V and 15 A respectively). It is thus possible to simulate a PV generator having a capacity of up to 750 W which can be increased to the kW range by simply having a power amplifier with higher capacity. The amplifier can also be used in another mode where it amplifies the characteristics of a solar cell so as to obtain the characteristics of a solar array.
5. Application Two typical loads are used as examples to demonstrate the performance of the computerized solar-array simulator. Figure 5 shows the operating 5.5
lO00w/m z
4.4
750 3.5
"3 5OO
•
Q
2.2
®
•
o
® ••
•
•
7.,S0 °
•o
oo o
VOLTRGE (V)
0
12
24
•
" "'"
56
48
Fig. 5. Array simulator with typical photovoltaic loads: @ @ 0 , operating points obtained with variable resistive load; [] [] m, operating curve of the m o t o r - p u m p load direct-coupled, with variation in illumination; o o®, operating curve of the m o t o r - p u m p load with d.c. voltage switching regulator, with variation in illumination.
389 points obtained for four different illuminations, at constant temperature, by varying a resistive load across the simulator. The parameters in the assumed model are determined from the manufacturer's data for a commercial panel (Photowatt PWP-800-73W/24V) consisting of 72 cells each having a diameter of 100 mm. The model supposes that two such panels are connected in parallel. Figure 5 also shows the operating points of a built-in d.c. permanent magnet m o t o r with volumetric pump (rated at 24 V and 100 W) at a constant head, direct-coupled and with a d.c. voltage switching regulator, obtained for different values of insolation. From the time at which either an alteration of load or a new value of a physical variable is entered, the speed of response for attaining the operating point with the given relative difference is less than 10 s. As can be seen from Fig. 5, the pumping starts at a b o u t 375 W m -2 with the switching regulator whereas the direct-coupled system pumps only at 525 W m -~. Figure 6 presents the array d.c. power o u t p u t for the two different configurations of pumping considered. Here, the simulation is conducted over a period of one day, at a constant head, with the assumption that the insolation profile has a sinusoidal distribution throughout the day, updated half-hourly. Thus =
950 sin(~(t
- -
6)/12~
(6)
144 '
los ;
o.
36
0
'
6
a.
.
.
. 10
.
.
TIME [HOLIRSI . . . . 12 14
16
18
Fig. 6. Array o u t p u t p o w e r on a day, with m o t o r - p u m p load at c o n s t a n t head and temperature: ' 4 4 4 , m a x i m u m available array o u t p u t p o w e r ; m m m, array o u t p u t p o w e r with directcoupling; o ® ®, array o u t p u t p o w e r with d.c. voltage switching regulator. (Np = 2, Ns = 72, R s = 0 . 0 2 2 ~ , B -1=0.031V, T=300K, a=0.253AW -1, ~ - - 0 . 7 1 9 × 1 0 - 3 K -1, S --- 78.6 cm 2, Ego = 1.21 eV, Cm = 0.212 × 1 0 4 A T -3 cm -2, k = 0.138 × 10 -22 JK-1).
390 w h e r e t is t h e t i m e i n h o u r s , a n d t h e t e m p e r a t u r e o f t h e a r r a y is a s s u m e d t o b e c o n s t a n t a t 3 0 °C t h r o u g h o u t t h e d a y .
6. Conclusions
A computerized solar array simulator incorporating programmable instruments, which can generally be found in any medium-sized laboratory, has been described. Sample simulation runs with typical photovoltaic loads are given. The introduction of the computer enhances the possibilities of studying PV systems. Their short- and long-term performance can be readily evaluated and predicted simply by feeding the insolation and temperature profiles into the computer; this would be impractical under real outdoor conditions. Use of the computer also allows the theoretical modelling techniques to be validated by directly testing the system sub-components with load units.
Acknowledgments The authors wish to thank Professor B. Lepley and Dr. P. H. Nguyen for their helpful suggestions.
References 1 E. R. Hoover, SOLCEL-II: An improved photovoltaic system analysis program, Proc. 14th Photovoltaic Specialists' Conf., San Diego, CA, January 7-10, 1980, IEEE, New York, 1980, pp. 1258 - 1261. 2 G. W. Hart, Residential photovoltaic system simulation, Proc. 16th Photovoltaic Specialists' Conf., San Diego, CA, September 27- 30, 1982, IEEE, New York, 1982, pp. 281 -288. 3 A. Laugier and J. A. Roger, Les Photopiles Solaires, Technique et Documentation, Paris, 1st edn., 1981, pp. 279 - 286. 4 L. Mirg, R. DeBlasio, G. A. Sullivan and R. P. Tomko, An advanced photovoltaic system simulator to demonstrate the performance of advanced photovoltaic cells and devices, Proc. 16th Photovoltaic Specialists' Conf., San Diego, CA, September 27 - 30, 1982, IEEE, New York, 1982, pp. 199 - 204. 5 L. H. Goldstein and G. R. Case, PVSS: A photovoltaic system simulation program, Sol. Energy, 21 (1978) 37 - 43. 6 G. Naaijar, Probl~mes d'adaptation des photopiles en vue d'applications terrestres, Acta Electron., 20 (1977) 165 - 185. 7 R.N. Hall, Silicon photovoltaic cells, Solid-State Electron. 24 (1981) 595 - 616.
383
M I C R O C O M P U T E R - C O N T R O L L E D S I M U L A T O R OF A PHOTOVOLTAIC G E N E R A T O R USING A P R O G R A M M A B L E VOLTAGE GENERATOR
T. E A S W A R A K H A N T H A N ,
J. BOTTIN, A. EL-SLASSI. R and S. R A V E L E T
Institut des Sciences de l'IngJnieur, Laboratoire d'Electronique et de Physique des Interfaces, UniversitJ de Nancy, Parc Robert Bentz, 54500 Vandoeuvre l$s Nancy
(France) (Received February 4, 1985; accepted July 16, 1985)
Summary A microcomputer-controlled simulator incorporating a programmable d.c. voltage generator, a programmable multimeter, and a power amplifier for physically simulating the power characteristics of solar photovoltaic generators based on a theoretical model are presented. Under software control in real time, with a linear interpolating iterative technique, the operating points of a photovoltaic generator-load system are established with sufficient accuracy. The main feature o f the simulator is its flexibility, since the influence of insolation, temperature and various array parameters on the array o u t p u t characteristics can be readily simulated. Physical simulations of a given photovoltaic generator with a variable resistance and a motor-pump load, direct-coupled and with an adaptor, are presented as examples.
1. Introduction The fact that photovoltaic (PV) generators respond differently than conventional ones necessitates a detailed study of would-be PV systems. Although the software programs [1,2] in which all system components are theoretically modelled simulate the performance of PV systems, the theoretical techniques must be validated through experimentation with such system sub-components as power conditioners. More often than not, in the absence of solar modules, it is necessary in an experimental study to use simulators which physically act as PV generators. In terms of reliability and convenience, greater control of a scheduled laboratory experiment is possible with a simulator than with natural sunlight. The methods generally used to devise such simulators [3,4] are the following: modifying a voltage source so that its internal resistance varies exponentially with current; amplifying the current and voltage of a solar 0379-6787/86/$3130
© Elsevier Sequoia/Printed in The Netherlands
384 cell; forming the PV generator equivalent circuit by using a constant current source and a diode-resistor network. Although such simulators have their merits, their limited flexibility in readily simulating the influence of insolation, temperature and various array parameters is an inconvenience that must be noted. Furthermore, there are potential problems of stability and linearity caused by the closed-loop electronic circuits. In this paper we introduce a solar-array simulator based on a Commodore CBM-4016 microcomputer with an Adret d.c. voltage generator, a Keithley multimeter (both programmable), and a power amplifier. A schematic diagram of the system is presented in Fig. 1. The operating points are approached for the changes in load, insolation and temperature, and also in various array parameters using a linear-interpolation iterative technique. In brief, the computer calculates successively the current and voltage at the intersection of the PV generator I - V c u r v e and a straight line through two points subsequently processed on the load-operating curve. It then programs the d.c. generator to apply the computed voltage across the load, reads the resulting current measured by the multimeter at its IEEE port, and tests the relative difference between the c o m p u t e d and measured currents. The program enters a waiting loop once the desired relative difference is attained. The extended flexibility is shown, n o t only by the elimination of closed-loop electronic circuits, but also by the possibility of simulating the influences of load, insolation and temperature by feeding them into the microcomputer through its i n p u t / o u t p u t ports or the keyboard. Moreover, the computer enables the characteristics of any type of solar panel to be reproduced once their parameters are known.
2. Model
o f the P V g e n e r a t o r
The current-voltage relation of a PV generator with Np parallel strings each comprising N s solar cells, with a one-diode equivalent electrical
AIO~
ompiifierLoad
.
I I
4
I I
User
?
i
L_
IEEE Port CBM-4016
Fig. 1. Schematic diagram of the simulator.
f TV
385
circuit assumed, is given by
I=Nplph--NploFexp~BIV+IRs~
(1)
where I and V are respectively the current and voltage at the o u t p u t of the PV generator, B -1 is the thermal voltage, and Rs is the series resistance of a solar cell [5]. The model assumes a negligible shunt conductance and the use o f identical cells operating under the same environmental conditions. The photocurrent Iph is a function of illumination ~b(W m -2) and temperature T. When only moderate temperatures (below 75 °C) and illuminations under 1000 W m -2 are considered, Iph may be written as Iph = C~(1 +
fJT)~S
(2)
where S is the area of a solar cell [6]. The constants ~ and ~ can be found in the experimental data or in the manufacturer's data for a solar panel. The saturation current I0 is only a function of temperature. It may be written [5, 7] as
Io = CmST3 exp(" E'°~ kT/
(3)
where Ego is the energy gap of the device material at 0 K, and k and Cm are the Boltzmann constant and the device specific constant respectively [5, 7]. It is assumed that Cm is independent of temperature.
3. Ascertaining the operating point Figure 2 shows the I-V curve of a solar array at a given temperature T, illumination ~ and load curve AB. The operating point P moves along the I-V curve between the open-circuit voltage Voc and the short-circuit current
~T
o
/B
vI
vz Vo~ ~v
Fig. 2. Principle of convergence from an initial point A to the operating point P through P0, P1 . . . . . P. The arrow indicates the converging direction.
386 Isc as the load varies. In order to ascertain the operating point the computer executes a BASIC program in real time. The main steps are outlined below. 3.1. Step 1: initialization
Once the computer calculates Voc, Isc, Iph and Io from the input physical variables and the array parameters, it programs the d.c. generator to apply a starting voltage VI (initially guessed to be about 0.25Voc) across the load and reads the resulting current It,1 at its IEEE port (see Fig. 2), measured and sent by the multimeter. If Ira1 is smaller than some predetermined lower limit relative to Isc, this step is repeated with a starting value of 0.5( V1 ÷ Voc). If I ~ 1 is relatively larger compared with Isc , the starting value is reduced to
0.5v . 3.2. Step 2: co m put at i on and testing
The c o m p u t e r calculates the current Icl and voltage V2 at the intersection P0 of the I - V curve and the straight line that runs through the origin and (V l, Im 1)- The generator then outputs V2 and the computer reads the current Ira2 through the load. The c o m p u t e r now tests the relative difference between the current measured Ira2 and c o m p u t e d Icl. If this difference is greater than 1%, the program repeats Step 2, this time computing the current and voltage at the intersection P1 of the array I - V curve and the straight line that runs through the last consecutively measured points on the load curve (V1, Im 1 ), (V2, Im: ). The straight line is represented by I = mV + c
(4)
where m and c are determined from the measured values, and c is zero for the very first iteration. The elimination o f V from eqns. (4) and (1) leads to the following nonlinear equation: I = N p I p h --NpI0(ex p [ S ( I ( 1 / m N s + Rs/Np) -- c/mNs} ] --1)
(5)
The program utilizes the second-order N e w t o n - R a p h s o n iterative technique to solve this equation, for which it deduces a suitable initial value. Once the current is determined, the voltage is computed from eqn. (4). With this approach the load curve is constantly traced and the convergence to the operating point is accelerated. In Fig. 2 only two such linear interpolating iterations are indicated. 3.3. Step 3: convergence when load changes
If the relative difference is less than 1%, which is defined as the criterion for the convergence to the operating point, the program enters and waits in a closed loop in which the computer constantly reads the current at its IEEE port and tests the relative difference. Whenever there is a variation in load such that the 1% limit is exceeded the program returns to Step 2; the iterations are repeated until the new operating point is reached. Figure 3 illustrates the convergence from P to the new operating point Q
387
I
[so 0++ Im]
....... :-----_-_---~
iml
.......................
ICl
Iml 7 Vl
V2 Voc
~V
e"
V2
v 1 vo~, Vo~ v
Fig. 3. Convergence f r o m P to the operating p o i n t Q through P0, PI, • • •, Q w h e n the load curve shifts f r o m AB to A ' B ' . Fig. 4. Convergence f r o m P to the operating p o i n t R through P0, P1 . . . . . illumination changes f r o m ¢ to ¢1.
R w h e n the
when the load-operating curve shifts from AB to A'B', indicating only two linear interpolating iterations.
3.4. Step 4: variations in illumination and temperature While waiting in the loop the program also enters the k e y b o a r d when the BASIC instruction GET is used. The keyboard loop allows the user to enter new values for temperature or illumination or both. For example, if a new illumination value ¢I is entered, the computer calculates Vocl, Iscl, Iphl and I01 anew and returns to Step 2. The iteration process continues until the computer arrives at the new operating point R with the desired relative difference. The program then enters the waiting loop where the microc o m p u t e r looks for the next alteration. Figure 4 illustrates the convergence with t w o such iterations for variation in illumination. 4. Remarks on system components
4.1. Programmable devices The C o m m o d o r e CBM-4016 microcomputer acts as the controller, and addresses and programs the Adret-103A d.c. voltage-current standard in its autoranging voltage m o d e by sending alphanumeric strings via the IEEE-488 bus. In the same manner it activates the programmable Keithley-195 with standard IEEE-488 interface to operate as a d.c. autoranging voltmeter with the desired reading rate. The multimeter could also be used as an ammeter to measure the current through the load directly. Instead, the current is determined from a measurement of the voltage across a k n o w n small shunt resistance. This avoids possibly erroneous reading resulting from the variation in internal resistance when the range of measurement in the current measuring m o d e changes automatically. The non-IEEE device used is the Watanabe plotter which is addressed and programmed through the user
388 port of CBM. It plots the operating current against voltage every time there is convergence to the operating point as a result of an alteration and thus allows the visualization of the I - V characteristics.
4.2. Power amplifier The Adret d.c. generator is limited in current to a maximum value of 110 mA. In order to simulate the solar panels which have important shortcircuit currents, a d.c. power amplifier is designed with the maximum output voltage and current (50 V and 15 A respectively). It is thus possible to simulate a PV generator having a capacity of up to 750 W which can be increased to the kW range by simply having a power amplifier with higher capacity. The amplifier can also be used in another mode where it amplifies the characteristics of a solar cell so as to obtain the characteristics of a solar array.
5. Application Two typical loads are used as examples to demonstrate the performance of the computerized solar-array simulator. Figure 5 shows the operating 5.5
lO00w/m z
4.4
750 3.5
"3 5OO
•
Q
2.2
®
•
o
® ••
•
•
7.,S0 °
•o
oo o
VOLTRGE (V)
0
12
24
•
" "'"
56
48
Fig. 5. Array simulator with typical photovoltaic loads: @ @ 0 , operating points obtained with variable resistive load; [] [] m, operating curve of the m o t o r - p u m p load direct-coupled, with variation in illumination; o o®, operating curve of the m o t o r - p u m p load with d.c. voltage switching regulator, with variation in illumination.
389 points obtained for four different illuminations, at constant temperature, by varying a resistive load across the simulator. The parameters in the assumed model are determined from the manufacturer's data for a commercial panel (Photowatt PWP-800-73W/24V) consisting of 72 cells each having a diameter of 100 mm. The model supposes that two such panels are connected in parallel. Figure 5 also shows the operating points of a built-in d.c. permanent magnet m o t o r with volumetric pump (rated at 24 V and 100 W) at a constant head, direct-coupled and with a d.c. voltage switching regulator, obtained for different values of insolation. From the time at which either an alteration of load or a new value of a physical variable is entered, the speed of response for attaining the operating point with the given relative difference is less than 10 s. As can be seen from Fig. 5, the pumping starts at a b o u t 375 W m -2 with the switching regulator whereas the direct-coupled system pumps only at 525 W m -~. Figure 6 presents the array d.c. power o u t p u t for the two different configurations of pumping considered. Here, the simulation is conducted over a period of one day, at a constant head, with the assumption that the insolation profile has a sinusoidal distribution throughout the day, updated half-hourly. Thus =
950 sin(~(t
- -
6)/12~
(6)
144 '
los ;
o.
36
0
'
6
a.
.
.
. 10
.
.
TIME [HOLIRSI . . . . 12 14
16
18
Fig. 6. Array o u t p u t p o w e r on a day, with m o t o r - p u m p load at c o n s t a n t head and temperature: ' 4 4 4 , m a x i m u m available array o u t p u t p o w e r ; m m m, array o u t p u t p o w e r with directcoupling; o ® ®, array o u t p u t p o w e r with d.c. voltage switching regulator. (Np = 2, Ns = 72, R s = 0 . 0 2 2 ~ , B -1=0.031V, T=300K, a=0.253AW -1, ~ - - 0 . 7 1 9 × 1 0 - 3 K -1, S --- 78.6 cm 2, Ego = 1.21 eV, Cm = 0.212 × 1 0 4 A T -3 cm -2, k = 0.138 × 10 -22 JK-1).
390 w h e r e t is t h e t i m e i n h o u r s , a n d t h e t e m p e r a t u r e o f t h e a r r a y is a s s u m e d t o b e c o n s t a n t a t 3 0 °C t h r o u g h o u t t h e d a y .
6. Conclusions
A computerized solar array simulator incorporating programmable instruments, which can generally be found in any medium-sized laboratory, has been described. Sample simulation runs with typical photovoltaic loads are given. The introduction of the computer enhances the possibilities of studying PV systems. Their short- and long-term performance can be readily evaluated and predicted simply by feeding the insolation and temperature profiles into the computer; this would be impractical under real outdoor conditions. Use of the computer also allows the theoretical modelling techniques to be validated by directly testing the system sub-components with load units.
Acknowledgments The authors wish to thank Professor B. Lepley and Dr. P. H. Nguyen for their helpful suggestions.
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