73

5th International Symposium „Topical Problems in the Field of Electrical and Power Engineering”,

Doctoral School of Energy and Geotechnology Kuressaare, Estonia, January 14 – 19, 2008

Comparison of a traditional diode photovoltaic model and simplified I-V curve based model

Lauris Bisenieks, Andrejs Stepanovs, Ilja Galkin

Riga Technical University, Institute of Industrial Electronics and Electrical Engineering, bisenieks@eef.rtu.lv; astepanov@eef.rtu.lv, gia@avene.eef.rtu.lv

Abstract This paper describes two different Pspice models of photovoltaic panel. The model development ways are described and evaluation is given. Results of simulation and experiments are presented and comparison of results is done.

Keywords

Photovoltaic panel, modelling, boost converter

Introduction

Solar radiation continuously incoming to the Earth and has an enormous energy potential. Even many times higher energy demand than today may be covered by the sun. The conversion of light into the electricity is done by means of photovoltaic (PV) panels. Nowadays they are quite widely spread and used in many applications from a calculator of couple of miliwatts to a power station of hundred kilowatts. However, this kind of the solar energy utilization is not so wide, as it could be. There are several reasons for that:

1) low efficiency of photovoltaic cell; 2) high cost of photovoltaic panels; 3) instability of the solar light (night or cloudy

weather); 4) problems with high volume electricity

accumulation; 5) additional conversion equipment is

necessary.

At the same time the cost of the PV elements, energy storages and semiconductor switches are getting lower, but their parameters – better. This especially regards efficiency of the solar cells that can be only 30% at the given time. Therefore the only factor that really limits the solar energy utilization is instability of light. That is why there is a need to combine photovoltaic arrays with some more reliable source of electricity, for example with electrical network.

An example of such system is elaborated and tested at the given time in Riga Technical University for the purpose to explore possibilities and efficiency of the solar energetics in Latvia. An array with 4 panels and tracker in the near future will be mounted on the roof of building of department of Power and

Electrical Engineering. While panels are not installed experiments are being done in laboratory with artificial lighting.

In order to attach the panels to electrical network and to a standard (220V, 50Hz) consumer of electrical energy is necessary a power converter. One of the ideas is to use topology of a half-bridge on-line uninterruptible power supply with solar batteries attached instead of (or together with) the other energy storage – battery or supercapacitor. In order to check the idea a PSpice model of the converter was built as close as possible to the real converter. Investigation of the model demonstrated difficulties of its implementation. The main question, however, is – if boost capability of the DC/DC converter is big enough to keep voltage of the DC-link at the high level. In order to answer this question a PSPICE model of the converter was build and simulation was done. Since the aim of the simulation is very practical it was decided to use as accurate models of elements as possible. At the same time limited calculation capacity does not allow exact simulation of the complete system. That is why only boost converter with PV array was simulated in order to estimate voltage of DC-link.

1 Pspice Models

The PSpice model of boost converter and two different models of photovoltaic array was build to make simulations.

Boost converter model (fig. 1) incorporate input coil L_L1 and its resistance R_L1, IGBT X1 – IRGP30B120, diode D1 – DSEP 29-12, DC link capacitor C_DC, IGBT driver circuit – E_D and R_Gate and load R_load.

Fig. 1. Boost converter

74

As a power supply (photovoltaic array) was tested 2 different models of photovoltaic arrays. To create the model of array was necessary to create the model

of photovoltaic cell and panel. Classical model of photovoltaic cell contains current source, diode, shunt and series resistances and capacitor (fig. 2) [1].

Fig. 2. Equivalent circuit for PV cell

This model can not be created if only standard parameters are known: short circuit current, open loop voltage, maximum power point voltage and current. Also additional parameters should be known, for example: internal series resistance, internal shunt resistance, capacitance of PN junction and diode characteristics. Producers of photovoltaic do not give such parameters in panel datasheets. All these parameters can be found experimentally. It must be noted that, if you haven’t cell for experiments, then parameters of individual cell can be found indirectly from panel parameters. Disadvantage of such recalculation is low precision of cell parameters. When all needed parameters were found the model of PV panel was created (Fig. 3).

Fig. 3. Diode based equivalent circuit of PV panel

In photovoltaic panel that was used for experiments are 32 cells connected in series, but in array that will be installed on the roof will be 4 panels. The model with all cells of the array will be very huge and difficult for modeling. To simplify the model of photovoltaic module the equivalent circuit of whole panel (fig. 4) was used. In this case the model has

smaller quantity of elements and experimentally measured parameters can be used directly in model. Twenty diodes instead of one were used because in PSpice it is not possible to make the diode with 20V forward voltage drop.

Fig. 4. Simplified equivalent circuit for PV panel

The hardest task in designing of PV panel/cell model is to create the diode with characteristics that gives required characteristic of photovoltaic panel/cell. “PSpice model editor” was used to create required diode model for PV module. I-V curve of this diode was made by reducing the voltage of the I-V curve of PV module twenty times. The model of diode with higher forward voltage drop was created intentionally to minimize quantity of diodes connected in series. Since the PV module curve already includes the series resistance impact, there is no need to include it additionally in the model. Shunt resistance should be included because there is no possibility to create diode I-V curve with sufficient slope in current source area. Simplified photovoltaic array model has 96 parts compare with 640 parts in usual one. This will reduce simulation time.

Second model of photovoltaic panel, that was tested, has even less parts. Whole photovoltaic panel is represented as voltage source E_T1 with real I-V curve of the photovoltaic panel (fig. 5). This voltage source includes not only diode characteristic, but also all resistances. Capacitor was added to this voltage source to improve model dynamics and substitute PN junction capacitance.

Fig. 5. Voltage source based model of PV panel

Points for voltage source can be taken from I-V characteristics from datasheet of photovoltaic panel (Fig. 6).

75

Fig. 6. I-V characteristic from PV datasheet [4]

But usually there are characteristics only for one temperature and for this reason points for developed model were taken from experimental curve (fig. 7). It guaranties that I-V characteristic will be in equal conditions (temperature, illumination) for both PV panel models and experiments.

Fig.7. Experemental I-V characteristic of a PV panel

2 Estimation of Photovoltaic Panel Parameters

To create PV panel model is necessary to know following parameters: open loop voltage, short circuit current, series resistance, shunt resistance and PN junction capacitance. First 2 parameters were found in producer datasheets and other parameters were found experimentally. Series resistance can be found dividing voltage drop on PV panel by current that flow through PV panel. At figure 8 is shown transient state of load connection. Open-circuit voltage (19V) after load connection drops to 16,5V. If tolerate that current increase is very short, it can be considered that point P1 is just after connection moment and that voltage of capacitor is still 19V.

23.07.10

5.161910=

−=

−=

I

UUR R

i(Ω) (1)

Fig. 8. Voltage and current curves that was used to determine series resistance of PV panel

After that 170 microseconds voltage is almost on the same value and before this time it drop and become

stable (fig. 9). This happens due to capacity of PN junction. Capacity can be calculated by equation 2:

V

ItC ac

∆

⋅∆=

_ (2)

Fig. 9. Voltage and current curves that was used to determine capacitance of PV panel

“Zone 2” can be explained with non-balancing illumination of photovoltaic panel. Confirmation of this can be seen on fig 10.

Fig. 10. Voltage and current curves.

On fig. 10 (a) is shown curves that were taken with 2 times smaller illumination (were used smaller number of projectors) that gave purer illumination balancing than on fig. 9. Effect of non-balanced illumination is higher. On fig. 10 (b) illumination is 1.5 times larger (were used larger number of projectors) that gave better illumination balancing than on fig. 9 and as can be seen, there are no effect of non-balanced illumination.

Point P1 was tolerated as transient state beginning because of that capacitor voltage can be considered to 19V. Voltage in point P2 is 14V, but it is voltage on load. Capacitor voltage in point P2 can be determined if to voltage in point P2 will be added voltage drop on internal panel resistance.

19.1623.05.9142222 =×+=×+=+= iRdRc RIVVVV (V) (3)

If substitute in equation (2) following values:

∆V=19-16.19=2.81V

∆ t=170us

76

AIII phaac 1.551.10_ =−=−= (4)

where acI _ - mean value of current in transient

state minus photocurrent that produce photovoltaic

panel, phI - photocurrent.

uFC 30981.2

1.510170 6

=⋅⋅

=

−

(5)

3 Pspice Simulation

The main problem that was investigated was ability of the PV array to ensure rated voltage over the DC-link. Since the inverter and rectifier of the on-line converter are half-bridge circuits, voltage of the DC-link must be doubled amplitude of the grid voltage or 800V. Voltage of 4 series connected PV batteries is up to 70V, but at maximum power point only 64V. Then gain of the boost converter must be about 12.5 that correspond to the duty cycle 0.93.

Simulation was done with two PV array models – diode based model and voltage source based model. In the beginning the current-voltage and power-voltage curves (fig. 11) was acquired of booth models to ensure that they are close to experimental ones.

Fig. 11. I-V and P-V curves: a) diode based model, b) voltage source based

Since voltage source model is based on experimental data directly, it is possible to assert that acquired curves are very close to real ones. Voltage source model gives maximum power of 350.9W at 64.8V, but diode one – 352.6W at 64.6V. In this case error do not exceed 0.5% and can be compared with measurements error in experiment. Such results allow perform future simulations of whole system.

As there were difficulties to realize boost converter control system with feedback, then were made decision to perform simulations with four constant duty cycles (0.67, 0.8, 0.9 and 0.93) and change load resistance. In such way were performed simulations with both models of PV arrays. On fig. 12. (a) are shown power-voltage curves of diode based model, but on fig. 12. (b) – curves of voltage source based one.

Fig. 12 Power-Voltage curves: a) diode based model, b) voltage source based model

As can be seen from diagrams, both models give similar results. Voltage source based model gives lower maximum power at higher voltage than diode based model. Maximum power levels and corresponding voltages are collected in table 1. Reason for such results is difference in photovoltaic array I-V curves. Diode based model gives higher power at lover voltage, but voltage source one – lower power at higher voltage.

Table 1. Maximum power points at different duty cycles

Duty cycle Power(W) Voltage(V) 0.67 342 189 0.8 343 306 0.9 339 568

Diode based model

0.93 333 877 0.67 336 189 0.8 324 312 0.9 336 580

Voltage source based model 0.93 313 909

4 Experimental Results

Some experiments were done to prove the simulation results. Since PV array and its tracker is not installed on the roof , there are no possibility to make experiments with four series connected modules at sunlight and results of experiments can be affected by the light instability. For these reasons halogen lamp illumination were made for one PV module and experiments were made with it. Experimentally acquired output power dependencies at duty cycles 0.67, 0.8, 0.9 and 0.93 are shown on fig. 13. There can be seen that maximum output power slightly decrease when duty cycle increase.

77

Fig. 13 Power-Voltage curves

Fig. 14 shows output power curves for PV array of four modules. These curves are directly calculated from experimental ones (fig. 13). Maximum output power point for experimental acquired curves is lower than for simulated ones. Reason for this difference is higher loses in boost converter due to 4 times lower input voltage than nominal (one module instead of four).

Fig. 14 Power-Voltage curves

Conclusions

Developed voltage source based PV model give similar results as diode based one. Since this model is easier in development it can be used in simulations where changing of light do not need to take into account. Simulation and experimental results show that proposed converter can be used for PV array connection to dc link of online UPS.

References

1 Luis Castaner, Santiago Silvester. “Modelling Photovoltaic Systems Using PSpice”, 2002

2 T. Markvart and L. Castaner, “Practical Handbook of Photovoltaics: Fundamentals and Applications”, 2003.

3 Muhammad H. Rashid, Power, “Electronics Handbook (Academic Press Series in Engineering” , 2001

4 http://www.sunpowercorp.com, datasheets

5 E. Matagne, R. Chenni, R. El Bachtiri, “A photovoltaic cell model based on nominal data only”, POWERENG2007, April 2007.

6 R. Chenni, M. Makhlouf, T. Kerbache, A. Bouzid, “A detailed method for photovoltaic cells”, ScienceDirect, December 2005.