- Email: [email protected]
Sizing standalone battery charging systems based on Photovoltaic (PVTCP) Temperature Crossing Points using Voltage Source Photovoltaic Model (VSPVM)
Solar Energy 136 (2016) 342–348
Contents lists available at ScienceDirect
Solar Energy journal homepage: www.elsevier.com/locate/solener
Sizing standalone battery charging systems based on Photovoltaic (PVTCP) Temperature Crossing Points using Voltage Source Photovoltaic Model (VSPVM) B. Kibirige Department of Physics and Engineering, University of Zululand, Private Bag x1001, KwaDlangezwa 3886, KZN, South Africa
a r t i c l e
i n f o
Article history: Received 14 December 2015 Received in revised form 8 June 2016 Accepted 4 July 2016
Keywords: Voltage Source Photovoltaic Model (VSPVM) Sizing standalone PV battery charging system Photovoltaic Temperature Crossing Points (PVTCP) Hot climate environments temperature effect
a b s t r a c t Rural and semi-rural communities in third world countries harness solar energy mostly by using standalone Photovoltaic (PV) battery charging systems. Basic electronics circuits that do not include direct current to direct current (DC-DC) voltage converters are employed. These provide raw voltage levels from the solar PV modules that sometimes charge batteries insufficiently, leading to shorter battery lives. By modelling the solar PV module using a voltage source circuit representation, the effects of temperature on the PV module voltage could easily be illustrated to these rudimentary trained communities that deal mostly with voltage sources and not current sources. A Voltage Source PV Model (VSPVM) was developed from the well understood PV cell mathematical model. Microsoft Excel (MSE) was used as the data fitting environment and the PSpice environment was used to capture the electronic circuit topology proposed for the VSPVM. Validating the model against experimental data fitted maximum power points within 5% of the experimental data. Observations made on I-V characteristics plotted on the same graph showed interesting patterns of crossing points referred to here as Photovoltaic Temperature Crossing Points (PVTCP). A low temperature cluster and a high temperature cluster which were indicative of thresholds of some sort were observed. For hot climate regions, the power point voltage which exists between the two clusters could be considered as a guide to the possible range within which a PV battery charging system should operation. Ó 2016 Elsevier Ltd. All rights reserved.
1. Introduction Disadvantaged rural and semi-rural communities in developing countries harness solar energy by using it in standalone Photovoltaic battery charging systems. For the most part, basic electronics setups are used. These do not include DC-DC voltage converters and provide raw voltage levels from the PV module. Tests carried out to investigate effects of increasing temperatures on I-V characteristics of solar photovoltaic systems have shown an increases in the short circuit current, a decrease in the open circuit voltage and an increase in the module series resistance (Xiao et al., 2004; Bashuhu and Nkundabakuru, 2006; and Pysch et al., 2007). PV modules in a battery charging system become hotter during the course of the day, leading to lower voltage levels available from them. If used in a standalone battery charging system, with no DC-DC voltage conversion, insufficient power may sometimes be provided leading to shorter battery lives. This phenomenon was observed in equatorial Uganda and in coastal E-mail address: [email protected] http://dx.doi.org/10.1016/j.solener.2016.07.004 0038-092X/Ó 2016 Elsevier Ltd. All rights reserved.
Zululand a region in sub-tropical South Africa with average ambient temperatures during hot seasons getting above 30 °C. Most solar modules are silicon and are good heat absorbers. This escalates temperature retained within the module. In order to provide these communities with convincing advice, experimental and simulation investigations were carried out on the extensively researched I-V characteristics of PV modules. This was done to establish possible novel trends that could be drawn on to determine of a workable solution. A voltage source circuit representation was used instead of the popular current source circuit representation (Tsai et al., 2008; Villalva et al., 2009; Bannet et al., 2012; Azooz and Sulyman, 2007; Millman and Halkias, 1972; Millman and Grabel, 1987), in order to emphasise the effects of high temperatures on the PV modules to the rudimentary trained rural/semi-rural communities. Both circuit representations are derived from well understood mathematical models; the only difference being in the circuit representation. Using a Voltage Source Photovoltaic Model (VSPVM), one is given an opportunity to illustrate the effects of temperature on the PV module voltage, giving a clearer understanding to a
B. Kibirige / Solar Energy 136 (2016) 342–348
community that deals with mostly voltage sources and not current sources. A basic standalone battery charging system designed to assist rural Zululanders in charging cell phone batteries was used as the basis for the investigation. Mid-day ambient temperatures could average above 30 °C. Therefore in Section 2, a brief overview on the battery charging regime of a Lithium-ion cell and the IV characteristics of a PV module are presented. In Section 3, the process of modelling the voltage source circuit representation is given. Experiments and simulations carried out in the investigations are presented in Section 4 and results, discussions and recommendations in Section 5. The summary and conclusion presented in Section 6 also mentions future work. 2. An overview of major system components One of the cell phone batteries targeted by the charging system was for the BlackBerry, Curve 8520. This phone uses a 3.7 V, 1150 mA h Lithium-ion battery. It is sold with a battery charger designed to provide a direct current (DC) output voltage of 5 V and a current of 700 mA from an Alternating Current (AC) voltage source of 220 Vrms/60 Hz utility supply. A CHN1-12P PV module was available for the design to provide conversion from radiant solar energy to DC electrical energy. It is a 12-cell polycrystalline module with Pmax = 1 W, Imp = 0.17 A, Vmp = 6.0 V, Isc = 0.34 A, Voc = 7.2 V at Standard Test Conditions (STC) and dimensions of 190 95 3.2 mm3. Keeping (2012) reports on the design of lithium-ion cells and alludes to their charging regime. Single cell Lithium-ion batteries are charged by a constant current, lower than the battery capacity current (1150 mA h, 4.3 W h for the Li-ion battery in the case study), until the open circuit voltage reaches 4.1–4.2 V (10% above battery capacity). This voltage is maintained as a constant source until the current drops to a threshold of 3% of the initial charging current. As the battery is used, it discharges and when it reaches a threshold of 65% of battery capacity (2.4–2.9 V), the system shuts down to protect the battery which is at risk at this point. Observations made on a solar battery charging system for the BlackBerry Lithium-ion battery, designed without a DC-DC converter, indicated that at maximum ambient temperatures observed around mid-day, in low latitude regions, it took longer to fully charge the cell phone battery and sometimes the solar charging system completely failed to charge the battery. A solar cell under a large reverse bias, generates a current I0 due to the thermal and photo generated minority charge carriers within the device. When the cell is illuminated, a short circuit current ISC , is generated. A load connected to the PV terminals acts to induce an electromotive force V that opposes the effects of the apparent photo voltage (open circuit voltage, V oc ). A current referred to here as Iv represents the diode forward current and it opposes the generated thermal and photo current (minority charge carrier current). The resulting total current (I) flowing in the cell is therefore expressed as:
I ¼ Isc þ I0 Iv
ð1:1Þ
Considering the fact that under irradiation, the short circuit current Isc is much greater than the reverse saturation current under dark conditions I0 , Eq. (1.2) below can be derived,
I ¼ Isc ð1 exp½ðV V oc Þ=gV T Þ
ð1:2Þ
g being the diode ideality factor for a single cell and V T the thermal voltage. Taking the system omhic losses into consideration, a series and parallel resistance Rp and Rs , are included to compensate for current leakages and voltage drops respectively. Manufacturers give lumped open circuit voltage and short circuit current values for an
343
entire PV module. Therefore, the ideality factor together with the series and parallel resistance of the entire module are multiples of the number of cells, n, and the respective parameter, leading to Eq. (1.3)
I ¼ Isc fð1 exp½ðV V oc IRS nRS Þ=gV T Þ ðV IRS nRS Þ=nRP g ð1:3Þ Eq. (1.3) is a well understood generalised mathematical model of a PV module. 3. Developing the Voltage Source PV Model (VSPVM) The circuit representation of Eq. (1.3) is shown in Fig. 1. The PV diode_cell and the Voc voltage source in Fig. 1 make up the essence of the PV cell. The voltage source, Voc, is temperature and irradiance dependant. It is the open circuit voltage of the PV cell/module. The PSpice parameters of the PV diode_cell in Fig. 1 were customised with a reverse saturation current equivalent to the photo current or short circuit (T sc ) and dependent on the irradiance and temperature, a junction voltage with a value that would render it negligible and a diode ideality factor g for the single cell or ng for the n-cell module. Rs and Rp are the lumped series and parallel leakage resistances of a single PV module. As can be deduced from the circuit in Fig. 1, the diode voltage is equivalent to the potential difference V V oc , where V is the propose battery voltage at the various stages of its charging cycle. 3.1. Model validation 3.1.1. Experiments Experiments were carried out to obtain I-V-characteristics for a single Copper Indium Gallium Selenide (CIGS) PV cell (CIG147A1Kc1) under standard test conditions (STC) and a 12-cell Si PV module (Model CHN1-12P) under the specified conditions. Conditions other than STC were used for the 12-cell Si PV module to establish how well the developed model wold perform under these conditions. The single CIGS solar cell was tested at 1000 W/m2 irradiation at a temperature of 25 °C. The cell had an area of 0.45 cm2. The voltage and current measurements were carried out using a four wire system, the Keithley 2400 source meter. The IV characteristic of the 12-cell Si PV module was obtained by varying the resistance at the module terminals from 0 to 10 kX. With the illumination at 850 000 lx (1244 W/m2), and a back surface temperature of 28 °C, the voltage across and the current through the resistance were measured using the Bs8252x Data Logging System V6.0.0.8s. 3.1.2. Model implementation Microsoft Excel and PSpice software environments were used in the validation of the proposed model. Using the Excel environment, the respective measured open circuit voltages, Voc, and short circuit currents, Isc, and the number of cells n = 1 and n = 12, for the single CIGS cell and the 12-cell CHN1-12P module, were substituted into Eq. (1.3). Then the diode equivalence factors g, the series and parallel resistance Rs and Rp were varied within the environment to achieve a good fit between experimental and simulated data. The circuit model shown in Fig. 1 was captured into the PSpice environment. A linear variable ramp voltage source, represents the voltage values of the load. The PVdiode_cell in Fig. 1. was edited and modified for each considered PV cell/module conditions by changing: the normally very small reverse saturation current (Io ) to the photo current (short circuit current Isc ), the junction voltage to a value that would render it negligible and the diode ideality factor g to the value determined by the fitting exercise carried out
344
B. Kibirige / Solar Energy 136 (2016) 342–348
Isc
I
Rs
PVdiode_cell
1.6
V Voc/Vph TD = 0 TF = 0 PER = V1 = -0.35 TR = 1 V2 = 0.8
Rp 0.6599
2k
0 Fig. 1. PSpice circuit representation for the single CIGS PV cell (CIG147A1Kc1).
surface temperature on the sizing of a cell phone battery charging system designed to charge a BlackBerry battery (Li-ion, 3.7 V with a capacity of 1150 mA h, 4.3 W h). The model was farther validated against experimental I-V data collected for different back surface temperatures.
Table 1 Fitted parameters of PV cell/module.
Number of cell (n) Irradiation/Illumination Temperature (T) Open circuit voltage (Voc) Short circuit current (Isc) Diode ideality factor (g) Parallel resistance (Rp ) Series resistance (Rs )
Single CIGS PV cell (CIG147A1Kc1)
12-cell Si PV module (Model CHN1-12P)
1 1000 W/m2 25 °C 0.6599 V 0.01399 A 2.1 2 kX 1.6 X
12 850 000 lx 28 °C 6.59 V 0.282 A 1.3 1 0
4.1. Experiments In order to assess the effects of temperature changes on the system, the PV module was exposed to a constant illumination source (850 000 lx to 1244 W/m2) and its back temperature allowed to rise by obscuring excessive heat losses from the module back surface using a heat insulating cover at the back of the module. The temperature at the back surface was measured at the beginning of each I-V data collection process using a J-type thermocouple. IV characteristics for back surface temperatures of 8 °C, 85 °C, 100 °C and 112 °C were obtained by varying the resistance at the module terminals from 0 to 10 kX. The voltage across and the current through the resistance were measured using the Bs8252x Data Logging System V6.0.0.8s.
Validating the model against experimental data fitted the maximum power points within 5% of the experimental data.
in the Excel environment. The values captured for the series and parallel resistances Rs and Rp , in Fig. 1, were equivalent to those determined in the Excel environment for each PV cell/module condition. 3.2. Results and discussions
4.2. Simulations Table 1 shows the measured and fitted values of the PV cell/modules that were studied while Fig. 2 shows their I-V characteristics observed from experiments and simulations.
Simulations conditioned to satisfy experimental procedures and conditions were carried out as part of the investigation. Results for both activities are given and discussed in Section 5. 5. Results and discussions
The model was deemed sufficient for further investigations. The VSPVM for the 12-cell Si PV module (Model CHN1-12P) was used as a tool to investigate the effects of the module back
The expressions from MS Excel fitted curves shown in Fig. 3 are used to extract the module parameters Rs , Rp and g shown in Table 2.
0.05
0.3
0.04
0.25
I_Pspice
0.03
Current (A)
Current (A)
4. Experiments and simulations in PV temperature investigations
I_Exp
0.02
I_xls
0.01 -0.4
0
-0.2 0 -0.01 -0.02
0.2
0.4
Voltage (V)
(a)
0.6
0.8
1
0.2
I_Pspice
0.15
I_Exp
0.1
I_xls
0.05 0
0
2
4
6
Voltage (V)
(b)
Fig. 2. IV characteristics from simulations and experiments for PV modules (a) single CIGS PV cell (CIG147A1Kc1) and (b) 12-cell Si PV module (Model CHN1-12P).
345
0.4
0.4
0.3
0.3
0.2
8_Ps_Ex
0.1
8_Exp
Current (A)
Current (A)
B. Kibirige / Solar Energy 136 (2016) 342–348
0.2
85_Ps_Ex
0.1
85_Exp
0
0 0
2
4
6
0
8
2
Voltage (V)
6
(b)
(a) 0.4
0.3
100_Ps_Ex
0.2
100_Exp
0.1
Current (A)
0.4
Current (A)
4
Voltage (V)
0.3
0 2
4
112_EXP
0.1
0 0
112_Ps_Ex
0.2
6
0
2 4 Voltage (V)
Voltage(V)
6
(d)
(c)
Fig. 3. IV characteristics from experiments (Exp) and from PSpice simulations (Ps_Ex); module parameters Rs, g, Voc and Isc are extracted from experimental data at back surface temperatures of (a) 8 °C, (b) 85 °C, (c) 100 °C and (d) 112 °C.
Table 2 Measured and fitted parameters of the 12-cell Si PV module (CHN1-12P). Back surface temperature
Illumination Open circuit voltage (Voc) Short circuit current (Isc) Diode ideality factor (g) Parallel resistance (Rp ) Series resistance (nRs ) Thermal voltage (V t Þ
12-cell Si PV module (Model CHN1-12P)
Table 4 Coefficients of temperature and PV module parameters (at 0 °C) for the CHN1 12P at 1244 W/m2.
8 °C
85 °C
100 °C
112 °C
a
b
c
d
g0
Rs0
V oc0
Isc0
860 000 lx 6.87 V 0.299 A 3 1 0X 0.0234
860 000 lx 5.73 V 0.333 A 2 1 3.8 X 0.0308
860 000 lx 5.62 V 0.337 1.77 1 4.236 X 0.0322
860 000 lx 5.45 V 0.354 1.6 1 4.6 X 0.0332
0:0134
0:0453
0:0139
0:0005
3:1127
0:2983
6:967
0:2938
Table 3 Equations representing parameter trends as the back surface temperature increases. CHN1 12P extracted equations Rs ðTÞ ¼ bT Rs0 gðTÞ ¼ aT g0 V oc ðTÞ ¼ cT þ V oc0 Isc ðTÞ ¼ dT þ Isc0
Rs ðTÞ ¼ 0:0453T 0:2983 gðTÞ ¼ 0:0134T 3:1127 V 0c ðTÞ ¼ 0:0139T þ 6:967 Isc ðTÞ ¼ 0:0005T þ 0:2938
Table 5 Extracted PV module parameters for the CHN1 12P at specified temperatures. Temp (°C)
Rs/cell (X)
g/cell
Isc (A)
Voc (V)
Vt (V)
8 25 50 85 100 112
0.005342 0.69517 0.163892 0.296017 0.352642 0.397942
3.0055 2.7777 2.4427 1.9737 1.7727 1.6119
0.2978 0.3063 0.3188 0.3363 0.3438 0.3498
6.8558 6.6195 6.272 5.7855 5.577 5.4102
0.024236 0.025703 0.027859 0.030878 0.032171 0.033206
5.2. IV characteristics and crossing points 5.1. Temperature coefficients Fig. 3 shows that the simulation results from the voltage source model were in good agreement with those from experiments. The parameter trends recorded in Table 3 were derived from the model fitting parameters recorded in Table 2 versus the recorded back surface temperature. a, b, c and d are coefficients of temperature for ideality factor g, series resistance Rs , open circuit voltage V oc and short circuit current Isc respectively. For the CHN1 12P, at a constant light intensity of 850 000 lx (1244 W/m2), the coefficients of temperature and the parameter Isc0 ; V oc0 ; Rs0 and g0 at 0 °C extracted from the parameter trends of Table 3 are given in Table 4 below. The voltage source parameters in Table 5, for the CHN1 12P module, at different back surface temperatures were determined using equations in Table 3. Customising the Voltage source model with the parameters in Table 5, the I-V characteristics for the indicated temperatures were collected and are shown in Fig. 4(a).
Crossing points were observed on the I-V characteristics plot presented in Fig. 5(a) and zoomed in as shown in Fig. 5(b). There are two clusters: a High Temperature Cluster (HTC) close to point (2.1 V, 0.326 A) a the Low Temperature Cluster (LTC) close to point (4.1 V, 0.289 A). Table 6 gives a summary of the points considered to be important to the subsequent discussion. It was also observed in Fig. 5 that the 50 °C I-V characteristic exists as a connecting curve between the two cluster points. On this characteristic at 2.1 V and 4.1 V, the current is 0.315 A and 0.275 A correspond to a power transfer of 0.662 W and 1.128 W respectively. 5.3. Discussions The observations made on the PV module parameters modelled in Microsoft Excel and captured and simulated in PSpice as a voltage source circuit model were in agreement with other researchers as reviewed in Section 1. For a constant light intensity, the back surface temperature of the PV module increased with
B. Kibirige / Solar Energy 136 (2016) 342–348
0.4
0.4
0.3
0.3
0.2 8_Ps 0.1
8_Exp
Current (A)
Current (A)
346
0
85_Ps 0.1
85_Exp
0 0
2
4
6
8
0
4
6
Voltage (V)
(a)
(b)
0.4
0.4
0.3
0.3
0.2 100_Ps 0.1
100_Exp 2
4
6
8
8
0.2 112_Ps
0.1
112_EXP
0
0 0
2
Voltage (V)
Current (A)
Current (A)
0.2
0
2
4
6
Voltage (V)
Voltage (V)
(c)
(d)
8
Fig. 4. IV characteristics from experiments (Exp) and from PSpice simulations (Ps); Module parameters Rs, g, Voc and Isc are estimated for the back surface temperatures of: (a) 8 °C, (b) 85 °C, (c) 100 °C and (d) 112 °C.
0.4
0.35
0.3
25_Ps 50_Ps
0.2
85_Ps 0.1
100_Ps 112_Ps
0 0
2
4
Current (A)
Current (A)
8_Ps
8_Ps 25_Ps 50_Ps
0.3
85_Ps 0.25 1.5
100_Ps 2
2.5
3
3.5
4
4.5
112_Ps
Voltage (V)
6
Voltage (V)
(a)
(b)
Fig. 5. IV characteristics for the estimated module parameters Rs, g, Voc and Isc at the indicated temperatures (8 °C, 25 °C, 50 °C, 85 °C, 100 °C and 112 °C).
Table 6 Voltage, current and power at the low temperature cluster, high temperature cluster and at maximum power points (MPP) for the 8 °C and 50 °C IV curves.
HCT At 50 °C LCT At 50 °C At 112 °C MPP 50 °C MPP 25 °C MPP 8 °C
Current (A)
Voltage (V)
Power (W)
0.326 0.315 0.289 0.275 0.191 0.264 0.259 0.255
2.1 2.1 4.1 4.1 4.1 4.3 4.8 5.2
0.685 0.662 1.185 1.128 0.783 1.137 1.243 1.327
time of exposure and there was an increase in the system’s series resistance, a decrease in the diode ideality factor while the system’s parallel resistance remained effectively big and did not bare significance on the system’s performance. Fig. 5(a) shows that with increasing back surface temperature, the module open circuit voltage decreased while its short circuit current increased. Also the increase in the system series resistance affects the gradient of the slope of the I-V as the voltage gets closer to the open circuit voltage of the PV module. The various changes in the PV module characteristics lead to interesting patterns in I-V characteristics (Fig. 5) such as crossing points.
5.3.1. Crossing points Crossing points in experimental data have been observed and used by various researchers in applied sciences. Giguere et al. (2002) used them to eliminate lift off effects from pulsed eddy currents materials analysis Kibirige (2012) used times of crossing in pulsed eddy current profile gauging application. In this study, temperature points of crossing in photovoltaic I-V characteristics were investigated to give an insight into possible solutions to the poor performance of PV modules in hot climate regions. The observations made on the solar battery charging system for the BlackBerry Lithium-ion battery introduced in Section 2 indicated that at maximum ambient temperatures observed around midday, in low latitude regions, it took longer to fully charge the cell phone battery and sometimes the solar charging system failed to charge the battery. When I-V characteristics for the different back surface temperatures were plotted on the same graph (Fig. 5), the observed crossing points represent equal voltage and current of the modules at two or more temperatures. Without a DC-DC voltage converter in the charging system, the HTC at a high flowing current of 0.326 A and a low voltage of low 2.1 V would not drive the battery charging process of the BlackBerry case study (Section 2). For the above design, a low temperature cluster (LTC) which existed at a voltage
B. Kibirige / Solar Energy 136 (2016) 342–348
1.4 1.3
Power (W)
1.2 P8_Ps
1.1
P25_Ps
1
P50_Ps
0.9
P85_Ps P100_Ps
0.8
P112_Ps
0.7 0.6
0
2
4
6
8
10
Voltage (V) Fig. 6. Power-Voltage characteristics of the Model CHN1 12P at the indicated back surface temperatures (8 °C, 25 °C, 50 °C, 85 °C, 100 °C, 112 °C).
of 4.1 V and a current of 0.289 A would support the battery charging process. Although the current at the LTC (0.298 A) was lower than that at the HTC (0.326), the power at the LTC was higher (1.185 W) than that at the HTC (0.685 W) indicating better performance at lower temperatures. The 50 °C I-V characteristic did not participate in the LTC and the HTC but existed as a connecting curve between the two clusters (Fig. 5(b)). At 4.1 V, a voltage required to sustain the constant voltage charging regime for the single cell Lithium ion battery, the corresponding current and voltage on the 50 °C I-V characteristic is 0.275 A and 1.128 W respectively (Table 6). At the HTC voltage of 2.1 V, the current and power were 0.315 A and 0.662 W respectively (see Fig. 6). For the recommended charging voltage of 4.1, the power at the 50 °C I-V characteristic (1.128 W) is much higher than that of the 112 °C I-V characteristic (0.783 W) indicating better performance at 50 °C. While that at the lowest considered temperature of 8 °C the power is (1.185 W). 5.3.2. Recommendations From the observations and discussions above, a single PV module, Model CHN1-12P, has the capacity to charge the BlackBerry Liion battery within a given range of its back surface temperatures. Although the current at the HTC is high (0.315 A), the voltage is low (2.1 V) and is not sufficient to sustain the charging of the targeted battery. The LTC has a lower current (0.289 A) at a higher voltage (4.1 V) and supports the battery charging regime. At the highest considered temperature of 112 °C, the current (0.191 A) and power (0.783 W) available at the recommended charging voltage of 4.1 V would definitely charge the battery for longer. The two temperature clusters are indicative of thresholds within which a PV battery charging system should operate. The 50 °C I-V characteristic joining the two clusters provides 0.275 A at 4.1 V and would charge a battery with a capacity of 1150 mA h/4.3 W h sufficiently. This suggests that PV back surface temperatures should be kept below 50 °C. Also, while it is suffices to use one Model CHN1-12P PV module for the system at temperatures lower than 50 °C, for high temperature conditions, to improve battery charging system would require to use more. 6. Summary and conclusion By modelling the solar PV module using a voltage source circuit representation, the effects of temperature on the PV module voltage could easily be illustrated to the rudimentary trained disadvantaged communities in the third world that deal mostly with voltage sources and not current sources. The sizing of a battery
347
charging solar system was based on a Voltage Source Photovoltaic Model (VSPVM) that was implemented using PSpice software environment. Expressions published by various researchers were summarised and interpreted to represent a PV module as voltage source in series with a customised reverse biased diode. The voltage source being temperature and irradiation dependant and the diode reverse saturation current made equivalent to the PV module short circuit current which is also temperature and irradiation dependant. Simulations were carried out in Excel to give definite values of the fitting parameters (g, Rp , Rs ). The model was validated in Microsoft excel and PSpice for a single CIGS PV cell (CIG147A1Kc1) and a 12-cell Si PV module (Model CHN1-12P). The single cell was tested under STC and the 12-cell module under conditions different from the STC as reported in Section 2 to assess performance under these conditions. The maximum power point for the model simulations carried out in both Microsoft Excel and PSpice was the same in both cases and was within 5% of the value obtained from experiments and was deemed useful for further investigations. The model was applied in the investigations carried out for sizing a battery charging system. Observations made on I-V characteristics plotted on the same graph showed interesting patterns of crossing points referred to Photovoltaic Temperature Crossing Points (PVTCP). A low temperature cluster and a high temperature cluster which were indicative of thresholds of some sort were observed. The 50 °C I-V characteristic neither participated in the high temperature cluster nor did it in the low temperature cluster. It represented a range of voltages between the two clusters. For hot climate regions, the power point voltage which exists between the two clusters could be considered as a guide to the possible range within which a PV battery charging system should operation. From observations and discussions, Section 5, it can be concluded that a single PV module, Model CHN1-12P, has the capacity to charge the BlackBerry Li-ion battery for back surface temperatures less than 50 °C. For back surface temperatures above the 50 °C, the system capacity to charge is lowered. While for low temperature conditions it was sufficient to use one Model CHN1-12P PV module for the system, for high temperature conditions, it would be necessary to use more. The work offers researchers from various disciplines and opportunity to become more attentive to crossing points in plotted results. It presents another approach to modelling PV cells/modules in electrical/electronic circuit topologies. It offers recommendations based on the observed crossing points to sizing PV standalone battery charging systems especially in hot environments. For future work novel techniques to realise the high efficient charging of batteries at high temperatures will be explored. Acknowledgements University of Zululand Research Office for the financial support provided during the course of the study. Appendix A. Supplementary material Supplementary data associated with this article can be found, in the online version, at http://dx.doi.org/10.1016/j.solener.2016.07. 004. References Azooz, A.A., Sulyman, J.M., 2007. Electronic control circuit for solar battery charging. Romanian Rep. Phys. 59, 101–111. Bannet, T., Zilouchian, A., Messenger, R., 2012. Photovoltaic modelling and converter topology considerations for MPPT purpose. Sol. Energy 86, 2029–2040.
348
B. Kibirige / Solar Energy 136 (2016) 342–348
Bashuhu, M., Nkundabakuru, P., 2006. Review and tests of methods for the determination of the solar cell junction ideality factors. Sol. Energy 81, 856– 863, Elsevier. Giguere, S., Lephine, B.A., Dubois, J.M.S., 2002. Pulsed eddy current technology: characterizing material loss with gap and lift-off variations. Res. Nondestruct. Eval. 13, 119–129. Keeping, S., 2012. A Designer Guide to Lithium Battery Charging.; visited 23 November 2015. Kibirige, B., 2012. An investigation of pulsed eddy currents for the development of a profile gauging system suitable for aluminium hot rolling mills. Mobile. wiredspace.wits.ac.za.
Millman, J., Grabel, A., 1987. Microelectronic. MsGraw-Hill, pp. 19–77. Millman, J., Halkias, C.C., 1972. Integrated Electronic: Analogue and Digital Circuit Systems. McGraw-Hill, pp. 49–84. Pysch, D., Mette, A., Glunnz, S.W., 2007. A review and comparison of different methods to determine the series resistance of solar cells. Sol. Cell Mater. Sol. cells, pp. 1698–1706, Elsevier. Tsai, H.L., et al., 2008, Development of Generalized Photovoltaic Model Using. Villalva, M.G., Gazoli, J.R., Filho, E.R., 2009. Comprehensive approach to modelling and simulation of photovoltaic arrays. IEEE Trans. Power Electr. 24 (5), 1198– 1208. Xiao, W., Dunford, W.G., Capel, A., 2004. A novel modelling method for photovoltaic cells, in: Annual IEEE Power Electronics Specialists Conference, pp. 1950–1956.
Contents lists available at ScienceDirect
Solar Energy journal homepage: www.elsevier.com/locate/solener
Sizing standalone battery charging systems based on Photovoltaic (PVTCP) Temperature Crossing Points using Voltage Source Photovoltaic Model (VSPVM) B. Kibirige Department of Physics and Engineering, University of Zululand, Private Bag x1001, KwaDlangezwa 3886, KZN, South Africa
a r t i c l e
i n f o
Article history: Received 14 December 2015 Received in revised form 8 June 2016 Accepted 4 July 2016
Keywords: Voltage Source Photovoltaic Model (VSPVM) Sizing standalone PV battery charging system Photovoltaic Temperature Crossing Points (PVTCP) Hot climate environments temperature effect
a b s t r a c t Rural and semi-rural communities in third world countries harness solar energy mostly by using standalone Photovoltaic (PV) battery charging systems. Basic electronics circuits that do not include direct current to direct current (DC-DC) voltage converters are employed. These provide raw voltage levels from the solar PV modules that sometimes charge batteries insufficiently, leading to shorter battery lives. By modelling the solar PV module using a voltage source circuit representation, the effects of temperature on the PV module voltage could easily be illustrated to these rudimentary trained communities that deal mostly with voltage sources and not current sources. A Voltage Source PV Model (VSPVM) was developed from the well understood PV cell mathematical model. Microsoft Excel (MSE) was used as the data fitting environment and the PSpice environment was used to capture the electronic circuit topology proposed for the VSPVM. Validating the model against experimental data fitted maximum power points within 5% of the experimental data. Observations made on I-V characteristics plotted on the same graph showed interesting patterns of crossing points referred to here as Photovoltaic Temperature Crossing Points (PVTCP). A low temperature cluster and a high temperature cluster which were indicative of thresholds of some sort were observed. For hot climate regions, the power point voltage which exists between the two clusters could be considered as a guide to the possible range within which a PV battery charging system should operation. Ó 2016 Elsevier Ltd. All rights reserved.
1. Introduction Disadvantaged rural and semi-rural communities in developing countries harness solar energy by using it in standalone Photovoltaic battery charging systems. For the most part, basic electronics setups are used. These do not include DC-DC voltage converters and provide raw voltage levels from the PV module. Tests carried out to investigate effects of increasing temperatures on I-V characteristics of solar photovoltaic systems have shown an increases in the short circuit current, a decrease in the open circuit voltage and an increase in the module series resistance (Xiao et al., 2004; Bashuhu and Nkundabakuru, 2006; and Pysch et al., 2007). PV modules in a battery charging system become hotter during the course of the day, leading to lower voltage levels available from them. If used in a standalone battery charging system, with no DC-DC voltage conversion, insufficient power may sometimes be provided leading to shorter battery lives. This phenomenon was observed in equatorial Uganda and in coastal E-mail address: [email protected] http://dx.doi.org/10.1016/j.solener.2016.07.004 0038-092X/Ó 2016 Elsevier Ltd. All rights reserved.
Zululand a region in sub-tropical South Africa with average ambient temperatures during hot seasons getting above 30 °C. Most solar modules are silicon and are good heat absorbers. This escalates temperature retained within the module. In order to provide these communities with convincing advice, experimental and simulation investigations were carried out on the extensively researched I-V characteristics of PV modules. This was done to establish possible novel trends that could be drawn on to determine of a workable solution. A voltage source circuit representation was used instead of the popular current source circuit representation (Tsai et al., 2008; Villalva et al., 2009; Bannet et al., 2012; Azooz and Sulyman, 2007; Millman and Halkias, 1972; Millman and Grabel, 1987), in order to emphasise the effects of high temperatures on the PV modules to the rudimentary trained rural/semi-rural communities. Both circuit representations are derived from well understood mathematical models; the only difference being in the circuit representation. Using a Voltage Source Photovoltaic Model (VSPVM), one is given an opportunity to illustrate the effects of temperature on the PV module voltage, giving a clearer understanding to a
B. Kibirige / Solar Energy 136 (2016) 342–348
community that deals with mostly voltage sources and not current sources. A basic standalone battery charging system designed to assist rural Zululanders in charging cell phone batteries was used as the basis for the investigation. Mid-day ambient temperatures could average above 30 °C. Therefore in Section 2, a brief overview on the battery charging regime of a Lithium-ion cell and the IV characteristics of a PV module are presented. In Section 3, the process of modelling the voltage source circuit representation is given. Experiments and simulations carried out in the investigations are presented in Section 4 and results, discussions and recommendations in Section 5. The summary and conclusion presented in Section 6 also mentions future work. 2. An overview of major system components One of the cell phone batteries targeted by the charging system was for the BlackBerry, Curve 8520. This phone uses a 3.7 V, 1150 mA h Lithium-ion battery. It is sold with a battery charger designed to provide a direct current (DC) output voltage of 5 V and a current of 700 mA from an Alternating Current (AC) voltage source of 220 Vrms/60 Hz utility supply. A CHN1-12P PV module was available for the design to provide conversion from radiant solar energy to DC electrical energy. It is a 12-cell polycrystalline module with Pmax = 1 W, Imp = 0.17 A, Vmp = 6.0 V, Isc = 0.34 A, Voc = 7.2 V at Standard Test Conditions (STC) and dimensions of 190 95 3.2 mm3. Keeping (2012) reports on the design of lithium-ion cells and alludes to their charging regime. Single cell Lithium-ion batteries are charged by a constant current, lower than the battery capacity current (1150 mA h, 4.3 W h for the Li-ion battery in the case study), until the open circuit voltage reaches 4.1–4.2 V (10% above battery capacity). This voltage is maintained as a constant source until the current drops to a threshold of 3% of the initial charging current. As the battery is used, it discharges and when it reaches a threshold of 65% of battery capacity (2.4–2.9 V), the system shuts down to protect the battery which is at risk at this point. Observations made on a solar battery charging system for the BlackBerry Lithium-ion battery, designed without a DC-DC converter, indicated that at maximum ambient temperatures observed around mid-day, in low latitude regions, it took longer to fully charge the cell phone battery and sometimes the solar charging system completely failed to charge the battery. A solar cell under a large reverse bias, generates a current I0 due to the thermal and photo generated minority charge carriers within the device. When the cell is illuminated, a short circuit current ISC , is generated. A load connected to the PV terminals acts to induce an electromotive force V that opposes the effects of the apparent photo voltage (open circuit voltage, V oc ). A current referred to here as Iv represents the diode forward current and it opposes the generated thermal and photo current (minority charge carrier current). The resulting total current (I) flowing in the cell is therefore expressed as:
I ¼ Isc þ I0 Iv
ð1:1Þ
Considering the fact that under irradiation, the short circuit current Isc is much greater than the reverse saturation current under dark conditions I0 , Eq. (1.2) below can be derived,
I ¼ Isc ð1 exp½ðV V oc Þ=gV T Þ
ð1:2Þ
g being the diode ideality factor for a single cell and V T the thermal voltage. Taking the system omhic losses into consideration, a series and parallel resistance Rp and Rs , are included to compensate for current leakages and voltage drops respectively. Manufacturers give lumped open circuit voltage and short circuit current values for an
343
entire PV module. Therefore, the ideality factor together with the series and parallel resistance of the entire module are multiples of the number of cells, n, and the respective parameter, leading to Eq. (1.3)
I ¼ Isc fð1 exp½ðV V oc IRS nRS Þ=gV T Þ ðV IRS nRS Þ=nRP g ð1:3Þ Eq. (1.3) is a well understood generalised mathematical model of a PV module. 3. Developing the Voltage Source PV Model (VSPVM) The circuit representation of Eq. (1.3) is shown in Fig. 1. The PV diode_cell and the Voc voltage source in Fig. 1 make up the essence of the PV cell. The voltage source, Voc, is temperature and irradiance dependant. It is the open circuit voltage of the PV cell/module. The PSpice parameters of the PV diode_cell in Fig. 1 were customised with a reverse saturation current equivalent to the photo current or short circuit (T sc ) and dependent on the irradiance and temperature, a junction voltage with a value that would render it negligible and a diode ideality factor g for the single cell or ng for the n-cell module. Rs and Rp are the lumped series and parallel leakage resistances of a single PV module. As can be deduced from the circuit in Fig. 1, the diode voltage is equivalent to the potential difference V V oc , where V is the propose battery voltage at the various stages of its charging cycle. 3.1. Model validation 3.1.1. Experiments Experiments were carried out to obtain I-V-characteristics for a single Copper Indium Gallium Selenide (CIGS) PV cell (CIG147A1Kc1) under standard test conditions (STC) and a 12-cell Si PV module (Model CHN1-12P) under the specified conditions. Conditions other than STC were used for the 12-cell Si PV module to establish how well the developed model wold perform under these conditions. The single CIGS solar cell was tested at 1000 W/m2 irradiation at a temperature of 25 °C. The cell had an area of 0.45 cm2. The voltage and current measurements were carried out using a four wire system, the Keithley 2400 source meter. The IV characteristic of the 12-cell Si PV module was obtained by varying the resistance at the module terminals from 0 to 10 kX. With the illumination at 850 000 lx (1244 W/m2), and a back surface temperature of 28 °C, the voltage across and the current through the resistance were measured using the Bs8252x Data Logging System V6.0.0.8s. 3.1.2. Model implementation Microsoft Excel and PSpice software environments were used in the validation of the proposed model. Using the Excel environment, the respective measured open circuit voltages, Voc, and short circuit currents, Isc, and the number of cells n = 1 and n = 12, for the single CIGS cell and the 12-cell CHN1-12P module, were substituted into Eq. (1.3). Then the diode equivalence factors g, the series and parallel resistance Rs and Rp were varied within the environment to achieve a good fit between experimental and simulated data. The circuit model shown in Fig. 1 was captured into the PSpice environment. A linear variable ramp voltage source, represents the voltage values of the load. The PVdiode_cell in Fig. 1. was edited and modified for each considered PV cell/module conditions by changing: the normally very small reverse saturation current (Io ) to the photo current (short circuit current Isc ), the junction voltage to a value that would render it negligible and the diode ideality factor g to the value determined by the fitting exercise carried out
344
B. Kibirige / Solar Energy 136 (2016) 342–348
Isc
I
Rs
PVdiode_cell
1.6
V Voc/Vph TD = 0 TF = 0 PER = V1 = -0.35 TR = 1 V2 = 0.8
Rp 0.6599
2k
0 Fig. 1. PSpice circuit representation for the single CIGS PV cell (CIG147A1Kc1).
surface temperature on the sizing of a cell phone battery charging system designed to charge a BlackBerry battery (Li-ion, 3.7 V with a capacity of 1150 mA h, 4.3 W h). The model was farther validated against experimental I-V data collected for different back surface temperatures.
Table 1 Fitted parameters of PV cell/module.
Number of cell (n) Irradiation/Illumination Temperature (T) Open circuit voltage (Voc) Short circuit current (Isc) Diode ideality factor (g) Parallel resistance (Rp ) Series resistance (Rs )
Single CIGS PV cell (CIG147A1Kc1)
12-cell Si PV module (Model CHN1-12P)
1 1000 W/m2 25 °C 0.6599 V 0.01399 A 2.1 2 kX 1.6 X
12 850 000 lx 28 °C 6.59 V 0.282 A 1.3 1 0
4.1. Experiments In order to assess the effects of temperature changes on the system, the PV module was exposed to a constant illumination source (850 000 lx to 1244 W/m2) and its back temperature allowed to rise by obscuring excessive heat losses from the module back surface using a heat insulating cover at the back of the module. The temperature at the back surface was measured at the beginning of each I-V data collection process using a J-type thermocouple. IV characteristics for back surface temperatures of 8 °C, 85 °C, 100 °C and 112 °C were obtained by varying the resistance at the module terminals from 0 to 10 kX. The voltage across and the current through the resistance were measured using the Bs8252x Data Logging System V6.0.0.8s.
Validating the model against experimental data fitted the maximum power points within 5% of the experimental data.
in the Excel environment. The values captured for the series and parallel resistances Rs and Rp , in Fig. 1, were equivalent to those determined in the Excel environment for each PV cell/module condition. 3.2. Results and discussions
4.2. Simulations Table 1 shows the measured and fitted values of the PV cell/modules that were studied while Fig. 2 shows their I-V characteristics observed from experiments and simulations.
Simulations conditioned to satisfy experimental procedures and conditions were carried out as part of the investigation. Results for both activities are given and discussed in Section 5. 5. Results and discussions
The model was deemed sufficient for further investigations. The VSPVM for the 12-cell Si PV module (Model CHN1-12P) was used as a tool to investigate the effects of the module back
The expressions from MS Excel fitted curves shown in Fig. 3 are used to extract the module parameters Rs , Rp and g shown in Table 2.
0.05
0.3
0.04
0.25
I_Pspice
0.03
Current (A)
Current (A)
4. Experiments and simulations in PV temperature investigations
I_Exp
0.02
I_xls
0.01 -0.4
0
-0.2 0 -0.01 -0.02
0.2
0.4
Voltage (V)
(a)
0.6
0.8
1
0.2
I_Pspice
0.15
I_Exp
0.1
I_xls
0.05 0
0
2
4
6
Voltage (V)
(b)
Fig. 2. IV characteristics from simulations and experiments for PV modules (a) single CIGS PV cell (CIG147A1Kc1) and (b) 12-cell Si PV module (Model CHN1-12P).
345
0.4
0.4
0.3
0.3
0.2
8_Ps_Ex
0.1
8_Exp
Current (A)
Current (A)
B. Kibirige / Solar Energy 136 (2016) 342–348
0.2
85_Ps_Ex
0.1
85_Exp
0
0 0
2
4
6
0
8
2
Voltage (V)
6
(b)
(a) 0.4
0.3
100_Ps_Ex
0.2
100_Exp
0.1
Current (A)
0.4
Current (A)
4
Voltage (V)
0.3
0 2
4
112_EXP
0.1
0 0
112_Ps_Ex
0.2
6
0
2 4 Voltage (V)
Voltage(V)
6
(d)
(c)
Fig. 3. IV characteristics from experiments (Exp) and from PSpice simulations (Ps_Ex); module parameters Rs, g, Voc and Isc are extracted from experimental data at back surface temperatures of (a) 8 °C, (b) 85 °C, (c) 100 °C and (d) 112 °C.
Table 2 Measured and fitted parameters of the 12-cell Si PV module (CHN1-12P). Back surface temperature
Illumination Open circuit voltage (Voc) Short circuit current (Isc) Diode ideality factor (g) Parallel resistance (Rp ) Series resistance (nRs ) Thermal voltage (V t Þ
12-cell Si PV module (Model CHN1-12P)
Table 4 Coefficients of temperature and PV module parameters (at 0 °C) for the CHN1 12P at 1244 W/m2.
8 °C
85 °C
100 °C
112 °C
a
b
c
d
g0
Rs0
V oc0
Isc0
860 000 lx 6.87 V 0.299 A 3 1 0X 0.0234
860 000 lx 5.73 V 0.333 A 2 1 3.8 X 0.0308
860 000 lx 5.62 V 0.337 1.77 1 4.236 X 0.0322
860 000 lx 5.45 V 0.354 1.6 1 4.6 X 0.0332
0:0134
0:0453
0:0139
0:0005
3:1127
0:2983
6:967
0:2938
Table 3 Equations representing parameter trends as the back surface temperature increases. CHN1 12P extracted equations Rs ðTÞ ¼ bT Rs0 gðTÞ ¼ aT g0 V oc ðTÞ ¼ cT þ V oc0 Isc ðTÞ ¼ dT þ Isc0
Rs ðTÞ ¼ 0:0453T 0:2983 gðTÞ ¼ 0:0134T 3:1127 V 0c ðTÞ ¼ 0:0139T þ 6:967 Isc ðTÞ ¼ 0:0005T þ 0:2938
Table 5 Extracted PV module parameters for the CHN1 12P at specified temperatures. Temp (°C)
Rs/cell (X)
g/cell
Isc (A)
Voc (V)
Vt (V)
8 25 50 85 100 112
0.005342 0.69517 0.163892 0.296017 0.352642 0.397942
3.0055 2.7777 2.4427 1.9737 1.7727 1.6119
0.2978 0.3063 0.3188 0.3363 0.3438 0.3498
6.8558 6.6195 6.272 5.7855 5.577 5.4102
0.024236 0.025703 0.027859 0.030878 0.032171 0.033206
5.2. IV characteristics and crossing points 5.1. Temperature coefficients Fig. 3 shows that the simulation results from the voltage source model were in good agreement with those from experiments. The parameter trends recorded in Table 3 were derived from the model fitting parameters recorded in Table 2 versus the recorded back surface temperature. a, b, c and d are coefficients of temperature for ideality factor g, series resistance Rs , open circuit voltage V oc and short circuit current Isc respectively. For the CHN1 12P, at a constant light intensity of 850 000 lx (1244 W/m2), the coefficients of temperature and the parameter Isc0 ; V oc0 ; Rs0 and g0 at 0 °C extracted from the parameter trends of Table 3 are given in Table 4 below. The voltage source parameters in Table 5, for the CHN1 12P module, at different back surface temperatures were determined using equations in Table 3. Customising the Voltage source model with the parameters in Table 5, the I-V characteristics for the indicated temperatures were collected and are shown in Fig. 4(a).
Crossing points were observed on the I-V characteristics plot presented in Fig. 5(a) and zoomed in as shown in Fig. 5(b). There are two clusters: a High Temperature Cluster (HTC) close to point (2.1 V, 0.326 A) a the Low Temperature Cluster (LTC) close to point (4.1 V, 0.289 A). Table 6 gives a summary of the points considered to be important to the subsequent discussion. It was also observed in Fig. 5 that the 50 °C I-V characteristic exists as a connecting curve between the two cluster points. On this characteristic at 2.1 V and 4.1 V, the current is 0.315 A and 0.275 A correspond to a power transfer of 0.662 W and 1.128 W respectively. 5.3. Discussions The observations made on the PV module parameters modelled in Microsoft Excel and captured and simulated in PSpice as a voltage source circuit model were in agreement with other researchers as reviewed in Section 1. For a constant light intensity, the back surface temperature of the PV module increased with
B. Kibirige / Solar Energy 136 (2016) 342–348
0.4
0.4
0.3
0.3
0.2 8_Ps 0.1
8_Exp
Current (A)
Current (A)
346
0
85_Ps 0.1
85_Exp
0 0
2
4
6
8
0
4
6
Voltage (V)
(a)
(b)
0.4
0.4
0.3
0.3
0.2 100_Ps 0.1
100_Exp 2
4
6
8
8
0.2 112_Ps
0.1
112_EXP
0
0 0
2
Voltage (V)
Current (A)
Current (A)
0.2
0
2
4
6
Voltage (V)
Voltage (V)
(c)
(d)
8
Fig. 4. IV characteristics from experiments (Exp) and from PSpice simulations (Ps); Module parameters Rs, g, Voc and Isc are estimated for the back surface temperatures of: (a) 8 °C, (b) 85 °C, (c) 100 °C and (d) 112 °C.
0.4
0.35
0.3
25_Ps 50_Ps
0.2
85_Ps 0.1
100_Ps 112_Ps
0 0
2
4
Current (A)
Current (A)
8_Ps
8_Ps 25_Ps 50_Ps
0.3
85_Ps 0.25 1.5
100_Ps 2
2.5
3
3.5
4
4.5
112_Ps
Voltage (V)
6
Voltage (V)
(a)
(b)
Fig. 5. IV characteristics for the estimated module parameters Rs, g, Voc and Isc at the indicated temperatures (8 °C, 25 °C, 50 °C, 85 °C, 100 °C and 112 °C).
Table 6 Voltage, current and power at the low temperature cluster, high temperature cluster and at maximum power points (MPP) for the 8 °C and 50 °C IV curves.
HCT At 50 °C LCT At 50 °C At 112 °C MPP 50 °C MPP 25 °C MPP 8 °C
Current (A)
Voltage (V)
Power (W)
0.326 0.315 0.289 0.275 0.191 0.264 0.259 0.255
2.1 2.1 4.1 4.1 4.1 4.3 4.8 5.2
0.685 0.662 1.185 1.128 0.783 1.137 1.243 1.327
time of exposure and there was an increase in the system’s series resistance, a decrease in the diode ideality factor while the system’s parallel resistance remained effectively big and did not bare significance on the system’s performance. Fig. 5(a) shows that with increasing back surface temperature, the module open circuit voltage decreased while its short circuit current increased. Also the increase in the system series resistance affects the gradient of the slope of the I-V as the voltage gets closer to the open circuit voltage of the PV module. The various changes in the PV module characteristics lead to interesting patterns in I-V characteristics (Fig. 5) such as crossing points.
5.3.1. Crossing points Crossing points in experimental data have been observed and used by various researchers in applied sciences. Giguere et al. (2002) used them to eliminate lift off effects from pulsed eddy currents materials analysis Kibirige (2012) used times of crossing in pulsed eddy current profile gauging application. In this study, temperature points of crossing in photovoltaic I-V characteristics were investigated to give an insight into possible solutions to the poor performance of PV modules in hot climate regions. The observations made on the solar battery charging system for the BlackBerry Lithium-ion battery introduced in Section 2 indicated that at maximum ambient temperatures observed around midday, in low latitude regions, it took longer to fully charge the cell phone battery and sometimes the solar charging system failed to charge the battery. When I-V characteristics for the different back surface temperatures were plotted on the same graph (Fig. 5), the observed crossing points represent equal voltage and current of the modules at two or more temperatures. Without a DC-DC voltage converter in the charging system, the HTC at a high flowing current of 0.326 A and a low voltage of low 2.1 V would not drive the battery charging process of the BlackBerry case study (Section 2). For the above design, a low temperature cluster (LTC) which existed at a voltage
B. Kibirige / Solar Energy 136 (2016) 342–348
1.4 1.3
Power (W)
1.2 P8_Ps
1.1
P25_Ps
1
P50_Ps
0.9
P85_Ps P100_Ps
0.8
P112_Ps
0.7 0.6
0
2
4
6
8
10
Voltage (V) Fig. 6. Power-Voltage characteristics of the Model CHN1 12P at the indicated back surface temperatures (8 °C, 25 °C, 50 °C, 85 °C, 100 °C, 112 °C).
of 4.1 V and a current of 0.289 A would support the battery charging process. Although the current at the LTC (0.298 A) was lower than that at the HTC (0.326), the power at the LTC was higher (1.185 W) than that at the HTC (0.685 W) indicating better performance at lower temperatures. The 50 °C I-V characteristic did not participate in the LTC and the HTC but existed as a connecting curve between the two clusters (Fig. 5(b)). At 4.1 V, a voltage required to sustain the constant voltage charging regime for the single cell Lithium ion battery, the corresponding current and voltage on the 50 °C I-V characteristic is 0.275 A and 1.128 W respectively (Table 6). At the HTC voltage of 2.1 V, the current and power were 0.315 A and 0.662 W respectively (see Fig. 6). For the recommended charging voltage of 4.1, the power at the 50 °C I-V characteristic (1.128 W) is much higher than that of the 112 °C I-V characteristic (0.783 W) indicating better performance at 50 °C. While that at the lowest considered temperature of 8 °C the power is (1.185 W). 5.3.2. Recommendations From the observations and discussions above, a single PV module, Model CHN1-12P, has the capacity to charge the BlackBerry Liion battery within a given range of its back surface temperatures. Although the current at the HTC is high (0.315 A), the voltage is low (2.1 V) and is not sufficient to sustain the charging of the targeted battery. The LTC has a lower current (0.289 A) at a higher voltage (4.1 V) and supports the battery charging regime. At the highest considered temperature of 112 °C, the current (0.191 A) and power (0.783 W) available at the recommended charging voltage of 4.1 V would definitely charge the battery for longer. The two temperature clusters are indicative of thresholds within which a PV battery charging system should operate. The 50 °C I-V characteristic joining the two clusters provides 0.275 A at 4.1 V and would charge a battery with a capacity of 1150 mA h/4.3 W h sufficiently. This suggests that PV back surface temperatures should be kept below 50 °C. Also, while it is suffices to use one Model CHN1-12P PV module for the system at temperatures lower than 50 °C, for high temperature conditions, to improve battery charging system would require to use more. 6. Summary and conclusion By modelling the solar PV module using a voltage source circuit representation, the effects of temperature on the PV module voltage could easily be illustrated to the rudimentary trained disadvantaged communities in the third world that deal mostly with voltage sources and not current sources. The sizing of a battery
347
charging solar system was based on a Voltage Source Photovoltaic Model (VSPVM) that was implemented using PSpice software environment. Expressions published by various researchers were summarised and interpreted to represent a PV module as voltage source in series with a customised reverse biased diode. The voltage source being temperature and irradiation dependant and the diode reverse saturation current made equivalent to the PV module short circuit current which is also temperature and irradiation dependant. Simulations were carried out in Excel to give definite values of the fitting parameters (g, Rp , Rs ). The model was validated in Microsoft excel and PSpice for a single CIGS PV cell (CIG147A1Kc1) and a 12-cell Si PV module (Model CHN1-12P). The single cell was tested under STC and the 12-cell module under conditions different from the STC as reported in Section 2 to assess performance under these conditions. The maximum power point for the model simulations carried out in both Microsoft Excel and PSpice was the same in both cases and was within 5% of the value obtained from experiments and was deemed useful for further investigations. The model was applied in the investigations carried out for sizing a battery charging system. Observations made on I-V characteristics plotted on the same graph showed interesting patterns of crossing points referred to Photovoltaic Temperature Crossing Points (PVTCP). A low temperature cluster and a high temperature cluster which were indicative of thresholds of some sort were observed. The 50 °C I-V characteristic neither participated in the high temperature cluster nor did it in the low temperature cluster. It represented a range of voltages between the two clusters. For hot climate regions, the power point voltage which exists between the two clusters could be considered as a guide to the possible range within which a PV battery charging system should operation. From observations and discussions, Section 5, it can be concluded that a single PV module, Model CHN1-12P, has the capacity to charge the BlackBerry Li-ion battery for back surface temperatures less than 50 °C. For back surface temperatures above the 50 °C, the system capacity to charge is lowered. While for low temperature conditions it was sufficient to use one Model CHN1-12P PV module for the system, for high temperature conditions, it would be necessary to use more. The work offers researchers from various disciplines and opportunity to become more attentive to crossing points in plotted results. It presents another approach to modelling PV cells/modules in electrical/electronic circuit topologies. It offers recommendations based on the observed crossing points to sizing PV standalone battery charging systems especially in hot environments. For future work novel techniques to realise the high efficient charging of batteries at high temperatures will be explored. Acknowledgements University of Zululand Research Office for the financial support provided during the course of the study. Appendix A. Supplementary material Supplementary data associated with this article can be found, in the online version, at http://dx.doi.org/10.1016/j.solener.2016.07. 004. References Azooz, A.A., Sulyman, J.M., 2007. Electronic control circuit for solar battery charging. Romanian Rep. Phys. 59, 101–111. Bannet, T., Zilouchian, A., Messenger, R., 2012. Photovoltaic modelling and converter topology considerations for MPPT purpose. Sol. Energy 86, 2029–2040.
348
B. Kibirige / Solar Energy 136 (2016) 342–348
Bashuhu, M., Nkundabakuru, P., 2006. Review and tests of methods for the determination of the solar cell junction ideality factors. Sol. Energy 81, 856– 863, Elsevier. Giguere, S., Lephine, B.A., Dubois, J.M.S., 2002. Pulsed eddy current technology: characterizing material loss with gap and lift-off variations. Res. Nondestruct. Eval. 13, 119–129. Keeping, S., 2012. A Designer Guide to Lithium Battery Charging.
Millman, J., Grabel, A., 1987. Microelectronic. MsGraw-Hill, pp. 19–77. Millman, J., Halkias, C.C., 1972. Integrated Electronic: Analogue and Digital Circuit Systems. McGraw-Hill, pp. 49–84. Pysch, D., Mette, A., Glunnz, S.W., 2007. A review and comparison of different methods to determine the series resistance of solar cells. Sol. Cell Mater. Sol. cells, pp. 1698–1706, Elsevier. Tsai, H.L., et al., 2008, Development of Generalized Photovoltaic Model Using. Villalva, M.G., Gazoli, J.R., Filho, E.R., 2009. Comprehensive approach to modelling and simulation of photovoltaic arrays. IEEE Trans. Power Electr. 24 (5), 1198– 1208. Xiao, W., Dunford, W.G., Capel, A., 2004. A novel modelling method for photovoltaic cells, in: Annual IEEE Power Electronics Specialists Conference, pp. 1950–1956.