A photovoltaic generator is a system composed of a series-parallel connection arrangement of the available. PV modules (solar panels). The power output of a ...
Reconfiguration Techniques of Partial Shaded PV Systems for the Maximization of Electrical Energy Production R. Candela*, V. Di Dio* , E. Riva Sanseverino*, P. Romano* * Università degli Studi di Palermo, viale delle Scienze (Italy)
Abstract -- In this paper, the research of the optimal layout of photovoltaic (PV) modules in a PV array giving the maximum output power under different shaded working conditions is carried out. The particular condition of non uniform solar exposition of the modules is analyzed. The study of the different configurations has been carried out starting from a circuital model used for the design of PV cells and for the simulation of the working behavior of PV arrays. The attained results appear to be interesting although the complexity of the problem in mathematical terms is huge when the number of panels is high. Moreover, the results confirm that this approach often allows to attain a higher electrical energy production compared to that attainable with PV arrays with a static layout.
The well-known drawbacks of the parallel connection of the cells, due to high output current, have been overcome in order to attain competitive configurations in terms of performance but also limiting the same current. II. THE MATHEMATICAL MODEL OF A PV CELL The typical equivalent circuit of a PV cell, shown in Fig. 1, is based on a diode and a current generator which are switched in parallel. The current source generates the photo current I1, which is directly proportional to the solar irradiance E. The voltage loss, that represent the external contacts of the PV cells, is expressed by a series resistor RS. Furthermore, leakage current is described by a parallel resistor RP, while V1 is the control voltage. Rs
Index Terms -- Photovoltaic cells, Solar power generation, Circuit optimization.
I. INTRODUCTION I1
The employ of photovoltaic arrays for the conversion of solar energy into electric energy is one of the most practical and efficient means for the usage of renewables. A photovoltaic generator is a system composed of a series-parallel connection arrangement of the available PV modules (solar panels). The power output of a PV system is expressed in Wp (Watt peak) and firstly depends on the different illumination levels, the module temperature and the shading condition. In this paper, the quantitative analysis of the efficiency of a PV system under different shaded working conditions is presented. In particular, we considered the common case, for large PV installations, of different states of shading of the system for a given number of panels. An 85% shading condition was considered [1] in all the test applications. The model for the single PV cell adopted has been taken from the literature [2, 3]. The basic knowledge for this study is the traditional circuit implementations of PV cells on the market and the modelling of elements with realistic features (contact resistance, shunt) and other components for the improvement of the performances (bypass diodes). Then the cell is analyzed from the circuital, mathematical and operational points of view. Then also the connection between the cells to compose a panel and finally the connection of PV panels in a photovoltaic array that maximizes the output energy in partial shading working conditions are analyzed.
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D1
V1 Rp
Fig. 1 Circuit model of a PV cell
The diode is the most important element of the circuit for the correct working of the PV cell model. Its presence indeed determines the exponential course of the current curve. Right on this curve the working point of the circuit model of the PV cell can be found. This point being the intersection between the load straight line and the curve showed in Fig. 2. The diode is thus the element characterising the non linear behaviour of the cell. The complete diode equation (1) is modelled through a set of parameters: (1)
where: - I0 is the scaling current, directly proportional to the cross section of the diode and generally of about 1015 A for low power applications [4, 5]. - q is the electron charge. - VD is the voltage applied at the diode. - n is the emission coefficient for diode. It depends on the manufacturing process with values ranging between 1 and 2. - k is the Boltzmann’s constant. - T is the absolute temperature in Kelvin.
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It is also often employed the constant VT = kT/q called scaling voltage, with a value of about 26 mV at ambient temperature (298 K or 25 °C). For this experiment the following values are taken I0 = 1,5⋅10-7 A, RS = 1⋅10-7 Ω, n = 1,5 [6]. Suitably combining the values of these elements a characteristic Power vs. Voltage similar to that of a commercial solar cell is attained (Fig. 2).
Therefore, in the reference configuration P-V characteristics have been obtained when one (Fig. 3), two (Fig. 4), then three (Fig. 5) and finally four panels (Fig. 6) are shaded. The obtained P-V characteristics can be assumed as the tool for the comparison with the alternative configurations considered.
Px=63 Wp Px=0,57 Wp
Fig. 3 One panel shaded, reference configuration. Fig. 2 P-V relation attained by the simulation of the circuit in fig. 1.
Px=45 Wp
III. THE PV ARRAY SIMULATION Considering the single cell model, a PV panel model have been implemented with 36 cells connected in series. Two different cases have been considered: with and without the placement of one by-pass diode in antiparallel every string of 12 cells (3 by-pass diode for each panel). These diodes have the main function to protect PV cells from thermal destruction in case of total or partial shading, broken cells, or cell string failures of individual solar cells while other cells are exposed to full light. In this way, if the string’s current decreases due to a partial shading of one or more cells, then the by-pass diode, forward biased, short-circuit the string. Therefore the low current circulation on one string does not affect the current circulation on the other strings composing the panel. The system configuration studied is made of matrices of panels partially shaded in different ways. The irradiated panels are characterised by a short-circuit current under Standard Test Conditions (illumination level of 1000 W/m2, a spectrum equivalent to AM 1,5 and 25°C module temperature at the test) equal to ISC = 1,2 A, the shaded ones by ISC = 0,18 A (reduction of 85%). In particular, the simplest case of squared matrix 2 x 2 has been analyzed with progressive shading of panels. In the analysis procedure, the reference configuration is the one with parallel connection of the four panels. It represents the optimal configuration for the maximization of the electrical energy production in case of full irradiated and partially shaded systems. Due to the relevant high output currents, alternative configurations must still be analyzed. In this way, the reduction of the currents in the system would limit the costs due to the conductors sections [7, 8, 9].
Fig. 4 Two panels shaded, reference configuration.
Px=27 Wp
Fig. 5 Three panels shaded, reference configuration.
Many simulations have been carried out considering the different four above described working conditions.
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The alternative configurations have been analyzed by means of the relevant P-V characteristics. Px=10 Wp
a)
Px=45 Wp
Fig. 6 Four panels shaded, reference configuration.
The first working condition comprises a single panel shaded. As we can see in Fig.7 the maximization of electrical energy production is obtained with a series of parallel of two panels. b) Fig. 8 Two shaded panels in parallel with two normally irradiated panels and then in series; a) connection’s scheme; b) P-V panels characteristic.
Finally, the last configuration is one with four shaded panels; the best solution found is one with a series of all the panels (Fig.10). a)
IV. SIMULATION RESULTS
Px=50 Wp
The reference configuration is the optimal one. Even with 85% shading of one or more panels we can attain the maximum output power, because the presence of a shaded panel does not affect the working conditions of the other panels. In the reference parallel configuration the by-pass diodes bring a negative effect on the overall producibility setting to zero the contribution of the shaded panel. In the real world applications this configuration is not adopted because the output current would be too high. It must be underlined that the static configurations usually employed include the use of by-pass diodes for series connected panels to avoid the mismatching. In this way, we don’t have any contribution of the shaded panels to the energy production. The simulations carried out show that in every shading conditions, making a reconfigurations of the panels connection, it is possible to obtain a larger energy production as compared to that obtainable using the static configurations. Indeed, these values of produced energy are comparable with those obtained in the reference configuration.
b) Fig. 7 One shaded panel in parallel to a not shaded one and in series to two other panels that are in parallel; a) connection’s scheme; b) P-V panels characteristic.
The second one is with two panels shaded. In this case, the solution maximizing the electrical energy production found is the one with a series of parallel of one shaded and one panel in full light as reported in Fig.8. The third configuration is made of three panels shaded. This time, the best solution found is the one with a series of one panel in full light and the parallel of three shaded panels (Fig.9).
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the one found in the reference configuration of Fig.4 and the peak value of power output is equal but with a much lower output current. The analysis has been carried out with an array of 2x2 panels. Extending the analysis to a larger number of cells or panels, the benefits would be much more important.
V. CONCLUSIONS a)
The scheme of parallel connection of all the panels of the system has been considered till now the best possible configuration. The problem, also, related to the high output current, requires the definition of new configurations. The configuration of the series of the parallels gives comparable performances to those detected in the reference configuration where the same output current is guaranteed between the blocks of panels (shaded and not in parallel) connected in series. This condition is ensured in all the symmetrical configurations, namely with the same number of shaded panels per block. A future development of this work is the implementation of an evolutionary optimization algorithm (genetic algorithm) in order to find in real time the optimal configuration of the panels in different shading conditions. In the evolutionary algorithm, the optimization variable is the layout string and the relevant quality is the energy on the conversion system.
Px=19 Wp
b) Fig. 9 Three shaded panels in parallel among them and in series with a normally irradiated panel; a) connection’s scheme; b) P-V panels characteristic.
REFERENCES [1] G. Velasco, J.J. Negroni, F. Guinjoan and R. Piqué: Some Considerations on Grid-Connected PV Systems Under Partial Shadowing Operation, SAAEI – EPF, CD ROM Seminar proceedings, September 2004, Toulouse. [2] Ching-Tsai Pan, Jeng-Yue Chen, Chin-Peng Chu and YiShuo Huang: A Fast Maximum Power Point Tracker For Photovoltaic Power Systems, The 25th Annual conference of de IEEE Industrial Electronics Society, 1999(IECON’92) Vol: 1 pg 390- 393; 0-7803-5735-3/99. [3] Geoff Walker: Evaluating MPPT Converter Topologies Using A Matlab PV Model, Power Conversion Conference 2002 Pcc Osaka 2002 Vol: 1, 2-5 April 2002 pg 322-327. [4] Franz J. Monssen: Orcad PSpice with Circuit Analysis , Prentice hall, 2001. [5] Adel S. SEDRA, Kenneth C. Smith: Microelectronic Circuit, 5th edition, Oxford University Press, 2003 [6] Wenham, S.R. Green, M. A., Watt, M. E.: Applied Photovoltaics” Center of Photovoltaic System and Devices, University of New South Wales, Sydney, Australia, 1994. [7] Charles G. Wright: Simulation of Solar Cell Properties with Electronic Circuit Simulation Software, Chuck Wright Consulting LLC, Round Rock, Texas [8] A. Gregg, T. Parker, R. Swenson: A real world examination of PV system design and performances, 31th IEEE Photovoltaic Specialists Conference, Orlando 2005. [9] N. J. C. M. van der Borg, M. J. Jansen: Energy loss due to shading in a BIPV application, 3rd Word Conference on Photovoltaic Energy Conversion, Osaka, Japan May 11-18 2003.
a)
Px=10 Wp
b) Fig. 10 Series of four shaded panels. a) connection’s scheme; b) P-V panels characteristic.
In particular, in the configuration of Fig. 8, namely the one in which the system puts together shaded and not shaded cells symmetrically, the power curve is similar to
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