- Email: [email protected]
Real-time simulation of photovoltaic modules
Pergamon
PII: SOO38-092X(96) 00008-4
Solar Enerav Vol. 56. No. 6, DD. 521-526. 1996 Co&right 8 1996 Elkier Science Ltd Printed in Great Britain. All rights reserved
0038-092X/96 $15.00 +O.OO
REAL-TIME
SIMULATION KAME KHOUZAM
Queensland
University
OF PHOTOVOLTAIC and KEITH HOFFMAN
of Technology, School of Electrical and Electronic GPO Box 2434, Brisbane, QLD 4001, Australia (Communicated
MODULES
by GERARD
Systems Engineering,
WRIXON)
Abstract-A photovoltaic (PV) array simulator, consisting of a computer controlled d.c. power supply producing up to 100 W and associated control software, was designed and developed to generate realtime current-voltage (I-Y) output characteristic curves of photovoltaic cells under simulated conditions. The system is also capable of modelling radiation damage due to high energy particles. The system comprises a pre-regulator, a switch-mode regulator, a computer interface, and modelling and control software. The control software uses feedback of the output voltage and current to iteratively converge to the actual operating point for the connected load. Simulation results match the expected theoretical calculations well. The main advantage of the simulator is its ability to simulate different types and sizes of arrays under varying illumination and temperature using actual loads. The system can be used to study the short-term and long-term performances of PV modules and to predict end-of-life efficiency. The simulator is a far more cost effective and reliable replacement for actual field testing. Copyright 0 1996 Elsevier Science Ltd.
a PV simulator using a programmable voltage generator which required a-priori information with regard to the connected load. This paper describes the development of both the hardware and software components of a computer controlled PV simulator. Modelling radiation damage due to high energy particles in space PV modules is also incorporated in this simulator.
1. INTRODUCTION
Although solar array characteristic curves can be modelled theoretically, the results must be validated through experimentation with various loads which include resistive, storage battery, d.c. motors, maximum power point tracker and inverter connected loads. At present this is usually accomplished by installing a prototype system and conducting field testing. Different types and sizes of arrays may be tested to find a suitable system for the particular load requirements. Field testing is costly, time consuming and depends heavily on prevailing weather conditions. Adequate security and weather protection must also be provided at the test site. Delays can also be caused due to bad weather and system failures. To overcome these problems, a PV array simulator may be used. Several methods of simulating PV arrays have been suggested in the past (Mrig et al., 1982). Some of the systems which have been proposed include: (i) modifying a voltage source so that its internal resistance varies exponentially with current; (ii) amplifying the current and voltage of a solar cell; and (iii) forming the PV generator equivalent circuit by using a constant current source and a diode-resistor network. Such simulators have some merits. However, their limited flexibility in readily simulating the influence of solar radiation, temperature and various array parameters is a serious drawback that has been noted. Easwarakhanthan et al. (1986) designed
2. PHOTOVOLTAIC SIMULATOR
The simulator utilizes a switched-mode stepdown or buck regulator (SMR) (Rashid, 1993), operating under computer (PC) control, to achieve output voltage and current characteristics that simulate a prescribed photovoltaic (PV) array. The characteristics of any type of PV array, its size as well as specific illumination, temperature conditions and PV aging, can be entered into the computer and the output of the regulator controlled to simulate these conditions. With continual measurement of the converter output voltage I$, and current Zpv, the desired PV characteristic can be obtained for varying load conditions, The specifications of the PV array simulator are: maximum open circuit voltage, Vpvoc = 100 V d.c. maximum short circuit current, I pvsc= 1 A d.c. switching frequency of SMR, f,,,, = 50 kHz As illustrated in Fig. 1, the converter and its 521
522
K. Khouzam
and K. Hoffman
cycle k of the SMR is given by: k+& dc
v,v + I,,&, Vdc
(1)
from which “PV
V k max = +???
and
dc
Fig. 1. Block diagram
of photovoltaic
array
control can be subdivided into two subsystems. They are: (i) a.c. to d.c. power supply; and (ii) computer control system consisting urement and interface circuits, software and interactive display.
simulator.
separate
of meascontrol
2.1. The a.c. to d.c. power supply The circuit diagram of the simulator power supply is shown in Fig. 2 and illustrates how the mains supply voltage is stepped down with an isolation transformer, rectified and smoothed to create an unregulated d.c. voltage V,,. The V,, is applied to the input of a switched-mode regulator (SMR) which operates at 50 kHz and further steps down the unregulated input voltage to a regulated d.c. output voltage of between 0 and 100 V. A parallel connected resistor R, allows the SMR to operate in its continuous conduction mode (Mohan et al., 1989) even when the output current I,, is zero. It is essential to maintain continuous current flow in the SMR inductor L,, so that the transfer function of the SMR remains linear over the complete operating range. An additional resistor R,, is added in series with the output to ensure that the simulator output voltage V,, can reach 0 V while still maintaining a reasonable SMR switching duty cycle. R,, is additionally used to measure the simulator output current I,, while also providing a degree of current limiting if a short circuit is applied to the output. Therefore, the duty
Rectificationand
Smoothing
I R kmin = pv,, Vdc
and for a duty cycle operating range of 0.2 5 k 5 0.8, vd, = 125 V d.c. and R,, z 21 0. 2.2. Computer control system Isolation amplifiers are used to interface VP, and I,, signals to the “Boston Technology” PC-30D data interface card inserted in the PC controller. Through the computer control algorithms and PV simulation equations (5) and (ll)-( 13), the output voltage of the SMR is made a function of the output current, i.e. V,,(Z,,). The mechanism for controlling the output voltage and current of the power supply is to first measure the current, for instance after a new load is applied, then calculate what the theoretical output voltage should be. The actual output voltage starts to change to become the theoretical value, and the current is measured again causing the theoretical voltage to be updated. This iterative process is repeated continuously and within a few milliseconds until the correct output voltage VP, and current I,, are within a small tolerance range for a particular load and specified PV array parameters. The control software is menu driven to allow the user to simulate any type and size of PV array of up to 100 V d.c. (at I,, = 0 A d.c.) and 1 A d.c. (at VP, = 0 V d.c.) output. The array parameters, as well as external illumination, temperature and aging (the latter due to radiation damage), of the PV array can be modified before and during operation. At the same time the PV array voltage-current characteristic curve may be defined in terms of either:
__J____----_-___A Switched Mode Regulator
Fig. 2. The a.c. to d.c. power supply.
Real-time
simulation
(i) theoretical array parameters: or (ii) interpolation between measured values of an actual array. The software options presented to the user as an on-screen display are shown in Fig. 3. 3. MATHEMATICAL
MODELLING
One of two methods can be used to simulate the output characteristics of the PV array. These are the parametric and the interpolation. 3.1. Parametric model This method assumes that all the array theoretical parameters are available. The output voltage is then calculated using these parameters and the illumination and temperature. The photocurrent I,, (A) of a single solar module is a function of temperature T (K), module constants CI and b, illumination 4 (W/m’) and the module surface area S (cm2) and is given by: ZPu= CI(1 + PT)@
(2)
of photovoltaic
modules
523
The saturation current is a function of the surface area and temperature and is given by:
(3) where the energy gap E,, (eV) of the device material is measured at 0 K, k is the Boltzmann constant (J/K) and C, is an array constant. The total output current of the solar panel is the difference between the photocurrent and the dark (diode) current and is given by:
I=N,I,,-N,Io(exp(B(g+?)--I) (4) where B (V/K) is the thermal voltage, R, (Q) is the series resistance of the solar module, Ns and Np are the number of modules in series and in parallel, respectively. Equation (4) can be rearranged to obtain the output voltage in terms
Set Illumination /Temperature
Use of Parametric / Intemolation Formula Change Array Parameters Set Protection Limits n Without Radiation Damage tion With Radiation Damaee Ouit
(4
(b) INTERPOLATION
Cc)
Cd)
Fig. 3. (a) Main menu; (b) menu to change radiation damage parameters; (c) menu to change array model parameters; (d) menu to change interpolation array model parameters.
parametric
524
K. Khouzam
of the output current: V=Ns
Bln (
(NJP” - 1) +l NJ0 [
1 ) -$
(5)
P
3.2. Interpolation model This method may be used when the theoretical parameters are unavailable. In this case three points are needed: the array open circuit voltage V,,, short circuit current I,, and the maximum power point voltage I&,, and current I,. In addition, an estimate of the series and shunt resistances can be calculated. These measurements are all conducted at a specified reference temperature TREF and an illumination 4 of 1000 W/m”. The resulting formulae can be determined for different illuminations and temperatures. Two constants are calculated from the three measured points:
G=(l-k)exp($$‘)
(6)
V mp -1 V OC
(7)
C2=
( > 1
In I-+ [
-
To simplify modelling the damaging effect of all radiation, the concept of an equivalent fluence is used. An equivalent fluence is the total number per unit area incident of a monoenergetic particle needed to cause the same degree of damage as a spectrum of light particles. Generally 1.0 MeV electrons is used. Using this quantity the effect of a particle on the cell short circuit current is given by (Lush and Gray, 1986): ZacJl= I,,, - Ci log
II/x1 [ l + Ik
Two parameters (Or) and (V,) are then calculated to account for the effect of temperature and radiation as follows: D, = a#(T - TREF)+ I,(# - 1)
(8)
V, = V+fi(T-
(9)
Then the output current and voltage are given by:
and
(12)
where I,,, = short circuit current density in (mA/cm’) at the beginning of life (BOL) of the cell (i.e. at $ = 0), Zsc,,,= short circuit current density in (mA/cm’) at a fluence of $, Ci is a constant and depends on the type of module, II/= irradiation fluence, $X = end of life (EOL) estimated fluence. A similar equation for voltage degradation was proposed by Khouzam (1988) and used in modelling (Lillington et al., 1988) the output voltage as: v-=y”-c.log[l+(~)o’g]
SC
TREF)+ RsD,
and K. Hoffman
(13)
where V,,, is the open circuit voltage at BOL, V,, is the open circuit voltage at a fluence of $, and C, is a constant and depends on the type of module. It should be noted that Ci and C, must be obtained using previous radiation damage modelling results. Using the new equations (12) and (13) for I,, and V,,, equations (10) and (11) can be modified to obtain the I-V characteristic curve for a solar array including radiation damage effect. 4. SIMULATION AND RESULTS
-b(T-
%EF)-RSDI
(11)
3.3. Radiation damage model The key limiting factor to solar cell efficiency in space is the high radiation trapped in the Van Allen Belt surrounding the earth. This radiation, made up of high energy particles penetrates the cells, disrupts the ordered lattice and introduces recombination centres, hence degrading the cell performance.
The characteristic Z-V curves for three sets of solar array modelling methods are plotted using the voltage and current outputs of the power supply when connected to a varying load resistance of O-1000 Q. Theoretical Z-V characteristic curves using the same parameters are also included for comparison. In these tests the load is varied in small steps and the output voltage and current measured once the system has reached a steady state after each load variation. The first two sets’ results, shown in Figs 4 and 5, use the parametric and interpolation methods, respectively, to obtain the I versus V characteristic curves. Individual parameters for
Real-time
simulation
0.8
2
y 0.6 B t: a 0.4 u 0.2 0 0
10
20
30
40
50
Voltage (V) Fig. 4. PV characteristics
using parametric
of photovoltaic
525
modules
When comparing the steady-state actual and the theoretical results for each set of tests it was observed that the two curves match very closely and indicate that the computer control system is operating correctly. When step load changes are applied to the PV simulator, the response time of the switched-mode regulator filter results in non-ideal I/-I transitions to the new operating point. With the aid of an external PID controller in the forward control loop these critically damped transitions could be restricted to less than 1 ms even with a maximum step load change. The PV simulator operates effectively when smoothly changing load conditions are applied.
formula.
5. CONCLUSION
0
10
Fig. 5. PV characteristics
20
30
40
using interpolation
SO
formula.
each test are listed in the Appendix. The third set of results shown in Fig. 6 incorporate the effect of radiation damage to the solar array. Parameters used in this test are listed in the Appendix. 1 ,
I
I
I
10
20
30
I
0.8
0 0
40
50
Voltage (V) Fig. 6. PV characteristics including radiation using interpolation formula.
damage
and
A PV array simulator consisting of a computer controlled d.c. power supply producing up to 100 W and associated control software can be used to generate the real-time 1-k’ output characteristic curves of solar panels under simulated conditions. This method offers advantages in simulating different types and sizes of arrays under any illumination and temperature condition in real-time using actual loads. Results obtained show that a good match between the calculated characteristics and the simulator characteristics can be achieved by using a fast response card and a smoothing filter. Hence, the simulator is a far more cost effective and reliable replacement for field or flight testing of modules. REFERENCES Easwarakhanthan T., Bottin J., El-Slassi A. and Ravelet S. (1986) Microcomputer-controlled simulator of a PV generator using a programmable voltage generator. Solar Cells 17, 383-390. Khouzam K.-Y. (1988) On-orbit performance modelling of back-gridded (bifacial) solar cells for space applications. Final report, Cleveland State University, work performed under NASA contract NAS3-24672. Lillington D., Kukulka J., Mason A., Sater B. and Sanchez J. (1988) Optimization of silicon 8 cm x 8 cm wrapthrough space station cells for on orbit operation. In Proceedings of 20th IEEE PV Specialists Conference, Dallas, pp. 934-939. Lush G. and Gray J. (1986) Two dimensional computer simulation of bilateral silicon solar cells. Final report, Purdue University, NASA TR-EE 87-37. Mirg L, DeBlasio R., O’Sullivan G. A. and Tomko T. (1982) An advanced PV system simulator to demonstrate the performance of advanced PV cells and devices. In Proceedings of 16th IEEE PV Specialists Conference, San Diego, pp. 1999204. Mohan N, Undeland T. M. and Robbins W. P. (1989) Power Electronics: Conoerters, Applications and Design, pp. 69-73. John Wiley & Sons, New York. Rashid M. H. (1993) Power Electronics Circuits, Deuices and Applications. 2nd edn, pp. 316-320. Prentice-Hall International, New Jersey.
526
K. Khouzam
and K. Hoffman
APPENDIX
Data used for simulation Parametric
parameters
a: 0.253 A/W
j? 0.000719/K Temperature, 7i 298.15 K Illumination, $: 500 W/m2 Module surface area, S: 40 cm2 Module constant, C,: 2120 A/K3/cm2 Energy gap at 0 Kelvin, E,,: 1.21 eV Boltzmann constant, k: 1.38 x 1O-23 J/K No. of parallel modules, NP: 1 No. of serial modules, Ns: 72 Thermal voltage, B: 0.031 V/K Module series resistance, R,: 0 i2 Interpolation parameters Array max. power point current, I,,: 0.8 A Array short circuit current, I,: 1 A Array max. power point voltage, I&,: 40 V Array open circuit voltage, K,: 45 V a: 0.253 A/W Illumination, 4: 500 W/m2
Initial temperature, T: 298.15 K Reference temperature, ‘J&: 298.15 K p: 0.000719/K Module series resistance, R,: 0 Cl Radiation damage parameters Array max. power point current, I,,: 0.8 A Array short circuit current, Isc: 1 A Array max. power point voltage, V,,: 40 V Array open circuit voltage, Vi 45 -v a: 0.253 A/W Illumination, 4: 500 W/m2 Initial temperature, 7! 298.15 K Reference temperature, TREF:298.15 K B: 0.0007 19/K Module series resistance, R,: 0 Q Short circuit current density, I,,: 1000 mA/cm2 Module constant, Ci: 0.05 Module constant, C,: 0.091 Irradiative fluence, +: 3 EOL fluence, IL.: 5
PII: SOO38-092X(96) 00008-4
Solar Enerav Vol. 56. No. 6, DD. 521-526. 1996 Co&right 8 1996 Elkier Science Ltd Printed in Great Britain. All rights reserved
0038-092X/96 $15.00 +O.OO
REAL-TIME
SIMULATION KAME KHOUZAM
Queensland
University
OF PHOTOVOLTAIC and KEITH HOFFMAN
of Technology, School of Electrical and Electronic GPO Box 2434, Brisbane, QLD 4001, Australia (Communicated
MODULES
by GERARD
Systems Engineering,
WRIXON)
Abstract-A photovoltaic (PV) array simulator, consisting of a computer controlled d.c. power supply producing up to 100 W and associated control software, was designed and developed to generate realtime current-voltage (I-Y) output characteristic curves of photovoltaic cells under simulated conditions. The system is also capable of modelling radiation damage due to high energy particles. The system comprises a pre-regulator, a switch-mode regulator, a computer interface, and modelling and control software. The control software uses feedback of the output voltage and current to iteratively converge to the actual operating point for the connected load. Simulation results match the expected theoretical calculations well. The main advantage of the simulator is its ability to simulate different types and sizes of arrays under varying illumination and temperature using actual loads. The system can be used to study the short-term and long-term performances of PV modules and to predict end-of-life efficiency. The simulator is a far more cost effective and reliable replacement for actual field testing. Copyright 0 1996 Elsevier Science Ltd.
a PV simulator using a programmable voltage generator which required a-priori information with regard to the connected load. This paper describes the development of both the hardware and software components of a computer controlled PV simulator. Modelling radiation damage due to high energy particles in space PV modules is also incorporated in this simulator.
1. INTRODUCTION
Although solar array characteristic curves can be modelled theoretically, the results must be validated through experimentation with various loads which include resistive, storage battery, d.c. motors, maximum power point tracker and inverter connected loads. At present this is usually accomplished by installing a prototype system and conducting field testing. Different types and sizes of arrays may be tested to find a suitable system for the particular load requirements. Field testing is costly, time consuming and depends heavily on prevailing weather conditions. Adequate security and weather protection must also be provided at the test site. Delays can also be caused due to bad weather and system failures. To overcome these problems, a PV array simulator may be used. Several methods of simulating PV arrays have been suggested in the past (Mrig et al., 1982). Some of the systems which have been proposed include: (i) modifying a voltage source so that its internal resistance varies exponentially with current; (ii) amplifying the current and voltage of a solar cell; and (iii) forming the PV generator equivalent circuit by using a constant current source and a diode-resistor network. Such simulators have some merits. However, their limited flexibility in readily simulating the influence of solar radiation, temperature and various array parameters is a serious drawback that has been noted. Easwarakhanthan et al. (1986) designed
2. PHOTOVOLTAIC SIMULATOR
The simulator utilizes a switched-mode stepdown or buck regulator (SMR) (Rashid, 1993), operating under computer (PC) control, to achieve output voltage and current characteristics that simulate a prescribed photovoltaic (PV) array. The characteristics of any type of PV array, its size as well as specific illumination, temperature conditions and PV aging, can be entered into the computer and the output of the regulator controlled to simulate these conditions. With continual measurement of the converter output voltage I$, and current Zpv, the desired PV characteristic can be obtained for varying load conditions, The specifications of the PV array simulator are: maximum open circuit voltage, Vpvoc = 100 V d.c. maximum short circuit current, I pvsc= 1 A d.c. switching frequency of SMR, f,,,, = 50 kHz As illustrated in Fig. 1, the converter and its 521
522
K. Khouzam
and K. Hoffman
cycle k of the SMR is given by: k+& dc
v,v + I,,&, Vdc
(1)
from which “PV
V k max = +???
and
dc
Fig. 1. Block diagram
of photovoltaic
array
control can be subdivided into two subsystems. They are: (i) a.c. to d.c. power supply; and (ii) computer control system consisting urement and interface circuits, software and interactive display.
simulator.
separate
of meascontrol
2.1. The a.c. to d.c. power supply The circuit diagram of the simulator power supply is shown in Fig. 2 and illustrates how the mains supply voltage is stepped down with an isolation transformer, rectified and smoothed to create an unregulated d.c. voltage V,,. The V,, is applied to the input of a switched-mode regulator (SMR) which operates at 50 kHz and further steps down the unregulated input voltage to a regulated d.c. output voltage of between 0 and 100 V. A parallel connected resistor R, allows the SMR to operate in its continuous conduction mode (Mohan et al., 1989) even when the output current I,, is zero. It is essential to maintain continuous current flow in the SMR inductor L,, so that the transfer function of the SMR remains linear over the complete operating range. An additional resistor R,, is added in series with the output to ensure that the simulator output voltage V,, can reach 0 V while still maintaining a reasonable SMR switching duty cycle. R,, is additionally used to measure the simulator output current I,, while also providing a degree of current limiting if a short circuit is applied to the output. Therefore, the duty
Rectificationand
Smoothing
I R kmin = pv,, Vdc
and for a duty cycle operating range of 0.2 5 k 5 0.8, vd, = 125 V d.c. and R,, z 21 0. 2.2. Computer control system Isolation amplifiers are used to interface VP, and I,, signals to the “Boston Technology” PC-30D data interface card inserted in the PC controller. Through the computer control algorithms and PV simulation equations (5) and (ll)-( 13), the output voltage of the SMR is made a function of the output current, i.e. V,,(Z,,). The mechanism for controlling the output voltage and current of the power supply is to first measure the current, for instance after a new load is applied, then calculate what the theoretical output voltage should be. The actual output voltage starts to change to become the theoretical value, and the current is measured again causing the theoretical voltage to be updated. This iterative process is repeated continuously and within a few milliseconds until the correct output voltage VP, and current I,, are within a small tolerance range for a particular load and specified PV array parameters. The control software is menu driven to allow the user to simulate any type and size of PV array of up to 100 V d.c. (at I,, = 0 A d.c.) and 1 A d.c. (at VP, = 0 V d.c.) output. The array parameters, as well as external illumination, temperature and aging (the latter due to radiation damage), of the PV array can be modified before and during operation. At the same time the PV array voltage-current characteristic curve may be defined in terms of either:
__J____----_-___A Switched Mode Regulator
Fig. 2. The a.c. to d.c. power supply.
Real-time
simulation
(i) theoretical array parameters: or (ii) interpolation between measured values of an actual array. The software options presented to the user as an on-screen display are shown in Fig. 3. 3. MATHEMATICAL
MODELLING
One of two methods can be used to simulate the output characteristics of the PV array. These are the parametric and the interpolation. 3.1. Parametric model This method assumes that all the array theoretical parameters are available. The output voltage is then calculated using these parameters and the illumination and temperature. The photocurrent I,, (A) of a single solar module is a function of temperature T (K), module constants CI and b, illumination 4 (W/m’) and the module surface area S (cm2) and is given by: ZPu= CI(1 + PT)@
(2)
of photovoltaic
modules
523
The saturation current is a function of the surface area and temperature and is given by:
(3) where the energy gap E,, (eV) of the device material is measured at 0 K, k is the Boltzmann constant (J/K) and C, is an array constant. The total output current of the solar panel is the difference between the photocurrent and the dark (diode) current and is given by:
I=N,I,,-N,Io(exp(B(g+?)--I) (4) where B (V/K) is the thermal voltage, R, (Q) is the series resistance of the solar module, Ns and Np are the number of modules in series and in parallel, respectively. Equation (4) can be rearranged to obtain the output voltage in terms
Set Illumination /Temperature
Use of Parametric / Intemolation Formula Change Array Parameters Set Protection Limits n Without Radiation Damage tion With Radiation Damaee Ouit
(4
(b) INTERPOLATION
Cc)
Cd)
Fig. 3. (a) Main menu; (b) menu to change radiation damage parameters; (c) menu to change array model parameters; (d) menu to change interpolation array model parameters.
parametric
524
K. Khouzam
of the output current: V=Ns
Bln (
(NJP” - 1) +l NJ0 [
1 ) -$
(5)
P
3.2. Interpolation model This method may be used when the theoretical parameters are unavailable. In this case three points are needed: the array open circuit voltage V,,, short circuit current I,, and the maximum power point voltage I&,, and current I,. In addition, an estimate of the series and shunt resistances can be calculated. These measurements are all conducted at a specified reference temperature TREF and an illumination 4 of 1000 W/m”. The resulting formulae can be determined for different illuminations and temperatures. Two constants are calculated from the three measured points:
G=(l-k)exp($$‘)
(6)
V mp -1 V OC
(7)
C2=
( > 1
In I-+ [
-
To simplify modelling the damaging effect of all radiation, the concept of an equivalent fluence is used. An equivalent fluence is the total number per unit area incident of a monoenergetic particle needed to cause the same degree of damage as a spectrum of light particles. Generally 1.0 MeV electrons is used. Using this quantity the effect of a particle on the cell short circuit current is given by (Lush and Gray, 1986): ZacJl= I,,, - Ci log
II/x1 [ l + Ik
Two parameters (Or) and (V,) are then calculated to account for the effect of temperature and radiation as follows: D, = a#(T - TREF)+ I,(# - 1)
(8)
V, = V+fi(T-
(9)
Then the output current and voltage are given by:
and
(12)
where I,,, = short circuit current density in (mA/cm’) at the beginning of life (BOL) of the cell (i.e. at $ = 0), Zsc,,,= short circuit current density in (mA/cm’) at a fluence of $, Ci is a constant and depends on the type of module, II/= irradiation fluence, $X = end of life (EOL) estimated fluence. A similar equation for voltage degradation was proposed by Khouzam (1988) and used in modelling (Lillington et al., 1988) the output voltage as: v-=y”-c.log[l+(~)o’g]
SC
TREF)+ RsD,
and K. Hoffman
(13)
where V,,, is the open circuit voltage at BOL, V,, is the open circuit voltage at a fluence of $, and C, is a constant and depends on the type of module. It should be noted that Ci and C, must be obtained using previous radiation damage modelling results. Using the new equations (12) and (13) for I,, and V,,, equations (10) and (11) can be modified to obtain the I-V characteristic curve for a solar array including radiation damage effect. 4. SIMULATION AND RESULTS
-b(T-
%EF)-RSDI
(11)
3.3. Radiation damage model The key limiting factor to solar cell efficiency in space is the high radiation trapped in the Van Allen Belt surrounding the earth. This radiation, made up of high energy particles penetrates the cells, disrupts the ordered lattice and introduces recombination centres, hence degrading the cell performance.
The characteristic Z-V curves for three sets of solar array modelling methods are plotted using the voltage and current outputs of the power supply when connected to a varying load resistance of O-1000 Q. Theoretical Z-V characteristic curves using the same parameters are also included for comparison. In these tests the load is varied in small steps and the output voltage and current measured once the system has reached a steady state after each load variation. The first two sets’ results, shown in Figs 4 and 5, use the parametric and interpolation methods, respectively, to obtain the I versus V characteristic curves. Individual parameters for
Real-time
simulation
0.8
2
y 0.6 B t: a 0.4 u 0.2 0 0
10
20
30
40
50
Voltage (V) Fig. 4. PV characteristics
using parametric
of photovoltaic
525
modules
When comparing the steady-state actual and the theoretical results for each set of tests it was observed that the two curves match very closely and indicate that the computer control system is operating correctly. When step load changes are applied to the PV simulator, the response time of the switched-mode regulator filter results in non-ideal I/-I transitions to the new operating point. With the aid of an external PID controller in the forward control loop these critically damped transitions could be restricted to less than 1 ms even with a maximum step load change. The PV simulator operates effectively when smoothly changing load conditions are applied.
formula.
5. CONCLUSION
0
10
Fig. 5. PV characteristics
20
30
40
using interpolation
SO
formula.
each test are listed in the Appendix. The third set of results shown in Fig. 6 incorporate the effect of radiation damage to the solar array. Parameters used in this test are listed in the Appendix. 1 ,
I
I
I
10
20
30
I
0.8
0 0
40
50
Voltage (V) Fig. 6. PV characteristics including radiation using interpolation formula.
damage
and
A PV array simulator consisting of a computer controlled d.c. power supply producing up to 100 W and associated control software can be used to generate the real-time 1-k’ output characteristic curves of solar panels under simulated conditions. This method offers advantages in simulating different types and sizes of arrays under any illumination and temperature condition in real-time using actual loads. Results obtained show that a good match between the calculated characteristics and the simulator characteristics can be achieved by using a fast response card and a smoothing filter. Hence, the simulator is a far more cost effective and reliable replacement for field or flight testing of modules. REFERENCES Easwarakhanthan T., Bottin J., El-Slassi A. and Ravelet S. (1986) Microcomputer-controlled simulator of a PV generator using a programmable voltage generator. Solar Cells 17, 383-390. Khouzam K.-Y. (1988) On-orbit performance modelling of back-gridded (bifacial) solar cells for space applications. Final report, Cleveland State University, work performed under NASA contract NAS3-24672. Lillington D., Kukulka J., Mason A., Sater B. and Sanchez J. (1988) Optimization of silicon 8 cm x 8 cm wrapthrough space station cells for on orbit operation. In Proceedings of 20th IEEE PV Specialists Conference, Dallas, pp. 934-939. Lush G. and Gray J. (1986) Two dimensional computer simulation of bilateral silicon solar cells. Final report, Purdue University, NASA TR-EE 87-37. Mirg L, DeBlasio R., O’Sullivan G. A. and Tomko T. (1982) An advanced PV system simulator to demonstrate the performance of advanced PV cells and devices. In Proceedings of 16th IEEE PV Specialists Conference, San Diego, pp. 1999204. Mohan N, Undeland T. M. and Robbins W. P. (1989) Power Electronics: Conoerters, Applications and Design, pp. 69-73. John Wiley & Sons, New York. Rashid M. H. (1993) Power Electronics Circuits, Deuices and Applications. 2nd edn, pp. 316-320. Prentice-Hall International, New Jersey.
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APPENDIX
Data used for simulation Parametric
parameters
a: 0.253 A/W
j? 0.000719/K Temperature, 7i 298.15 K Illumination, $: 500 W/m2 Module surface area, S: 40 cm2 Module constant, C,: 2120 A/K3/cm2 Energy gap at 0 Kelvin, E,,: 1.21 eV Boltzmann constant, k: 1.38 x 1O-23 J/K No. of parallel modules, NP: 1 No. of serial modules, Ns: 72 Thermal voltage, B: 0.031 V/K Module series resistance, R,: 0 i2 Interpolation parameters Array max. power point current, I,,: 0.8 A Array short circuit current, I,: 1 A Array max. power point voltage, I&,: 40 V Array open circuit voltage, K,: 45 V a: 0.253 A/W Illumination, 4: 500 W/m2
Initial temperature, T: 298.15 K Reference temperature, ‘J&: 298.15 K p: 0.000719/K Module series resistance, R,: 0 Cl Radiation damage parameters Array max. power point current, I,,: 0.8 A Array short circuit current, Isc: 1 A Array max. power point voltage, V,,: 40 V Array open circuit voltage, Vi 45 -v a: 0.253 A/W Illumination, 4: 500 W/m2 Initial temperature, 7! 298.15 K Reference temperature, TREF:298.15 K B: 0.0007 19/K Module series resistance, R,: 0 Q Short circuit current density, I,,: 1000 mA/cm2 Module constant, Ci: 0.05 Module constant, C,: 0.091 Irradiative fluence, +: 3 EOL fluence, IL.: 5