Energy Fuels 2010, 24, 6126–6130 Published on Web 10/15/2010
: DOI:10.1021/ef1006275
Optimum Load Matching by an Array Reconfiguration in Photovoltaic Generators F. Z. Zerhouni,* M. Zegrar, M. T. Benmessaoud, A. Boudghene Stambouli ,* and A. Midoun D epartement d’Electronique, Facult e G enie Electrique Universit e des Sciences et de la Technologie Mohamed Boudiaf d’Oran, (U.S.T.M.B.O) BP 1505, Oran El M’Naouer, Oran, Alg erie Received May 11, 2010. Revised Manuscript Received August 22, 2010
The arrangement of modules of a photovoltaic generator “PVG” depends largely on the application. The number of modules in series in a branch and the number of branches are linked to the output voltage and current required. For a fixed number of photovoltaic modules, the maximum power is constant whatever is the configuration adopted. The operating power is dependent on the device working conditions such as the insulation, the temperature, and the load. The work presented in this article is focused on the determination of the optimal configuration of the PVG, given a fixed number of modules. Our aim is to extract the highest power of the direct coupling between the PVG and the load. In this paper, we present a new method, which consists of determining on line and in real time which configuration is best whatever is the load and the working conditions and switch the PVG into that configuration. The presented method is based on the use of the data processor. Some parameters describing PV modules have been stocked on EPROM. Very simple calculations allowed to decide which configuration is appropriate for the load whatever the work conditions. This method is particulary appropriate for all direct coupling between a PVG and a load especially for the pumping system. Results that have been obtained experimentally confirm our theoretical analysis.
mismatch would lead to a lower efficiency of the overall system.1-6 The output current and voltage vary as a function of the weather conditions such as the insulation, temperature,7,8 as well as the connected load. To overcome the mismatch problem, different methods have been proposed.7-17 In refs 12 and 13 is presented a technique for finding the irradiance levels for optimum switching of photovoltaic (PV) powered water pumping systems operating with a multistage
1. Introduction Alternate energy systems are in high demand to minimize the dependence on foreign oil imports. They reduce significant capital investments for newer centralized power generating units and lower environmental pollution and maintenance. Solar energy is the world’s major renewable energy resource. Photovoltaic “PV” power can be generated from the sun in temperate or tropical locations and in urban or rural environments. A “PV” array is an important alternate energy source. The PV systems involve the direct conversion of sunlight into electricity without any intervention of fuel combustion engines. PV devices are solid state; therefore, they are rugged and simple in design and require very little maintenance. Photovoltaic arrays consist of many cells connected together to provide required terminal voltage and current ratings. The photovoltaic systems exploit the sun energy at various ends. They are highly reliable and constitute a nonpolluting source of electricity, which can be appropriate for many applications. The panels lack movable parts and require minimal maintenance. They neither contaminate nor produce any noise because they do not consume fuel at all. PV is uniquely scalable and is the only energy source that can supply power on a scale of milliwatts to megawatts from an easily replicated modular technology with excellent economies of scale in manufacture. In a directly coupled system, it is important to match the load to the PVG, otherwise the power loss resulting from this
(3) Khouzam, K. Y. The load matching approach to sizing photovoltaic systems with short-term energy storage. Sol. Energy 1994, 53 (5), 403–409. (4) Kalaitzakis, K. Optimum PV system dimensioning with obstructed solar radiation. Renewable Energy 1996, 7 (1), 51–56. (5) Gautam, N. K.; Kaushika, N. D. Reliability evaluation of solar photovoltaic arrays. Sol. Energy 2002, 72 (2), 129–141. (6) Badescu, V. Simple optimization procedure for silicon-based solar cell interconnection in a series-parallel PV module. Energy Convers. Manage. 2006, 47, 1146–1158. (7) Benghanem, M. Low cost management for photovoltaic systems in isolated site with new IV characterization model proposed. Energy Convers. Manage. 2009, 50, 748–755. (8) Khouzam, K. Optimum load matching in direct coupled PV power systems- Application to resistive loads. IEEE Trans. Energy Convers. 1990, 5 (2), 265–270. (9) Kaldellis, K.; Zafirakis, D.; Kondili, E. Optimum autonomous stand-alone photovoltaic system design on the basis of energy pay-back analysis. J. Energy 2009, 34 (9), 1187–1198. (10) Enrique, J. M.; Duran, E.; Sidrach-de-Cardona, M.; And ujar, J. M. Theoretical assessment of the maximum power point tracking efficiency of photovoltaic facilities with different converter topologies. Sol. Energy 2007, 81, 31–38. (11) Salas, V; Olias, E; Barrado, A; lazaro., A. Review of the maximum power point tracking algorithms for stand alone photovoltaic systems. J. Sol. Energy Mater. Sol. Cells 2006, 90, 1555–1578. (12) Salameh, Z. M.; Mulpur, A. K.; Dagher, F. Two stage electrical array reconfiguration controller. J. Photovoltaic Energy 1990, 44, 51–55. (13) Salameh, Z. M.; Chaozi L. Optimum switching points for array reconfiguration controller. 21st IEEE Photovoltaic Conference, Kissimee, FL, 1990; pp 971-976. (14) Munoz, F. J.; Almonacid, G.; Nofuentes, G.; Almonacid., F. A new method based on charge parameters to analyse the performance of stand alone photovoltaic systems. J. Sol. Energy Mater. Sol. Cells 2006, 90, 1750–1763.
*To whom correspondence should be addressed. Telephone/Fax: 41 56 03 29 or 56 03 01. E-mail:
[email protected] (F.Z.Z.); aboudghenes@ yahoo.com (A.B.S.). (1) Khouzam, K.; Khouzam, L.; Groumbos, P. P. Optimum matching of loads to the photovoltaic array. Sol. Energy 1991, 46 (2), 101–108. (2) Groumbos, P. P.; Papageorgiou, G. An optimum load management strategy for stand-alone photovoltaic power systems. Sol. Energy 1991, 46 (2), 121–128. r 2010 American Chemical Society
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Energy Fuels 2010, 24, 6126–6130
: DOI:10.1021/ef1006275
Zerhouni et al.
Figure 1. One-diode model of a PV cell D is the p-n junction; Rs is the intrinsic series resistance of the solar array; Rsh is the equivalent shunt resistance; I is the output current; V is the output voltage; Iph is the generated current; Id is the diode current; Vd is the diode voltage; and Is is the current through Rsh.
electrical array reconfiguration for a constant load. It reconfigures the PVG to be in parallel connection at a low irradiance level and in series connection at a high irradiance level. This method is limited for insulation changes, and the temperature factor is not considered. In another hand, the study is for a specific load and is not applicable if the load changes. In this case, the reference will change. So, it is necessary to make recourse to the simulation at each load change to decide about the commutation moment. The proposed method is particularly appropriated for all direct coupling between a PVG and a load. It is applied to all different loads regardless of the working conditions in real time. Figure 2. Different characteristics of the PVG: (a) I-V characteristic for different insulation values; (b) I-V characteristic for different temperatures values.
2. Solar Array Characteristics The solar cell is the basic unit of the photovoltaic generator. The solar cell is the device that transforms the sun’s rays or photons directly into electricity. There are various models of solar cells made with different technologies. These models have variable electrical and physical characteristics depending on the manufacturer. The element which is most commonly used in the fabrication of solar cells is silicon. The electric power generated by a solar array swing depends on the solar radiation “insulation” and temperature. The solar array is a nonlinear device and can be represented as a current source model, as shown in Figure1.7,8,15 Rs is the intrinsic series resistance of the solar array whose value is usually very small. Rsh is the equivalent shunt resistance of the solar array whose value is usually very large. In general, the output current of a solar array is a function of the insulation Es and the temperature T, as given by the following equation:7,8,15 " # V þ Rs I -1 ð1Þ I ¼ Icc - Io exp AUT UT ¼
KT q
thermal voltage, and A is the ideality factor for a p-n junction. Figure 2 illustrates the simulated characteristic curves for solar arrays at different insulations and different temperatures.15 The PV array has an optimum operating point called the maximum power point (MPP), which varies according to cell temperature and insulation level. In order to get the maximum power from the PV, a maximum power point tracker (MPPT) can be used. In Figure 2a, the optimal power points are represented by the (Iopt-Vopt) curve. From these characteristic curves, it is observed that the output characteristics of the solar array are nonlinear and vitally affected by the solar radiation and/or temperature. 3. Principle of the Reconfiguration Method A few years ago, solar arrays were connected to various loads through two ways. The first method is the direct coupled method, in which the solar array output power is delivered directly to the loads. This method cannot automatically track the MPPs of the solar array when the insulation or temperature changes. The load parameters or solar array parameters must be carefully selected for the direct coupled method. The second method is maximum power point tracker (MPPT) control, which continuously matches the output characteristics of the solar array to the input characteristics of the converters. Many works have been done previously for the improvement of the photovoltaic’s use.7-17 The power required for an application and the module’s types as well as the insulation are the main factors which determine the total modules (Nt) needed to build a PVG. However, the PVG’s configuration is the modules number in series in branch (Ns) and the branches number in parallel (Np), which depends on the output voltage and current required by the load. As an example, two modules can be connected either in series (Np = 1, Ns = 2) to obtain a high voltage and a low current or in parallel (Np = 2, Ns = 1)
ð2Þ
where I and V are the output current and output voltage of the solar array, respectively; Icc is the generated current under a given insulation; Io is the saturation current of a solar array; q is the electron charge; K is Boltzmann’s constant, UT is the (15) Zerhouni, F. Z. Developpement et optimization d’un generateur energetique hybride propre a base de PV-PAC. These de doctorat, Institut d’Electronique, USTO, 2009. (16) Appelbaum, J. The operation of loads powered by separate sources or by a common source of photovoltaic cells. IEEE Trans. Energy Convers. 1989, 4 (3), 351–357. (17) Mousazadeh, H.; Keyhani, A.; Javadi, A.; Mobli, H.; Abrinia, K.; Sharifi, A. A review of principle and sun-tracking methods for maximizing solar systems output. Renewable Sustainable Energy Rev. 2009, 13, 1800–1818.
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: DOI:10.1021/ef1006275
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Figure 3. PVG and load characteristics P-V.
Figure 5. The P-V PVG and load characteristics.
configuration depending on Es greater or less than 300 W/m2.15 If however the PVG is used to supply a variable load, then this method is not sufficient.18,19 In this case, the reference will change. 4. Configuration of a PVG The number of modules necessary to build a PVG depends on the required power, the types of modules used, and finally the operating conditions (insulation, temperature, humidity). However, with a given number of modules Nt, many different configurations may be adopted depending on the output voltage and required current for the load. With Nt equal to 12, it is possible to have six configurations whereas with Nt equals 24 or 30, eight configurations are possible. However, it is important to note that not all the configurations are convenient and therefore only two or three configurations are recommended to make the system efficient for a large area of applications. The other reason to select a restricted number of configurations is related to practical implementation of the proposed method. Indeed to go from one configuration to another one, some switches are opened and some others are closed to change the connections between the different modules of the PVG. Also as the number of configurations increases, the number of the switches increases and therefore both the load and the complexity of the system increase. To improve this technique, it is important to design a flexible system which can be adapted to large types of loads and under different operating conditions. The mismatch losses in a directly coupled load to a PVG are as a result reduced.
Figure 4. ηg variations against Es.
to obtain a low voltage and a high current. Nevertheless, the maximum power available in both cases is the same. As the modules number Nt increases, the possible configuration numbers increase. To explain the reconfiguration method principle, a PVG made of 45 modules is assumed. It is easy to check that six configurations are possible. For illustration purposes, two configurations are selected. The first configuration consists of 9 branches in parallel where each branch is made of 5 modules connected in series (Np Ns = 9 5); whereas the second configuration consists of 5 branches in parallel with 9 modules in series in each branch (Np Ns=5 9). The PVG power variations against its output voltage (P-V) for the two cases are shown in Figure 3. On the same figure is plotted the load’s (motor pump) P-V characteristics. In order to compare the two configurations, a quality of load matching coefficient ηg may be defined as ηg ¼ P1 =Popt
ð3Þ
where Pl is the operating power under given working conditions and Popt is the PVG optimum power under the same operating conditions. The coefficient ηg has been calculated for the two configurations and under different insulations at 25 °C. The results are shown in Figure 4. The variable η1 corresponds to configuration Np Ns = 9 5, and η2 corresponds to configuration Np Ns = 5 9. It is clear from the figure that for the insulation Es less than 300 W/m2 (noted 30%), the first configuration is best suited for this load. However, for insulation higher than 300 W/m2, the second configuration should be used. Therefore, if the load is constant, the insulation changes. So, it is possible to monitor only this parameter and switch onto the appropriate
5. Basics for the Proposed Method In Figure 5, the PVG characteristics for two different configurations (Np Ns = 2 3 and 1 6) as well as that of two different loads Za and Zb are plotted. In this case, the insulation and temperature are kept constant. As it can can be seen the power corresponding to point A1 is higher than that of point A2, which means that the first configuration (2 3) provides better load matching for this load than the second configuration (1 6). Whereas for load Zb, the power on point B1 is higher than that of point B2, which means that in this case, the second configuration is better. It is then necessary to select on line and in real time, the PVG appropriate configuration for a given load and under given working conditions in order to reduce the mismatch losses.16 Figure 5 shows that the two P-V PVG characteristics intersect at point “P”. On this operating point, either configurations could be used. Point “P” is taken as a reference. For loads where their operating points are at the left handside of point “P”, configuration 1 (noted series configuration) should
(18) Xiao, W.; Magnus, G. J.; Lind, W. G. Dunford and Antoine Capel. Real-Time Identification of Optimal Operating Points in Photovoltaic Power System. IEEE Trans. Ind. Electron. 2006, 53 (4), 1017– 1026. (19) Ikegami, T.; Maezono, T.; Nakanishi, F.; Yamagata, Y.; Ebihara, K. Estimation of equivalent circuit parameters of PV module and its application to optimal operation of PV system. Sol. Energy Mater. Sol. Cells 2001, 67, 389–395.
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: DOI:10.1021/ef1006275
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Figure 8. System components. Figure 6. Icom variation against Es for several T.
Figure 7. Vcom variation against insulation for several T.
Figure 9. Practical I-V results at Es = 780W/m2, T = 27 °C.
be used. Also, for all loads with operating points situated at the right handside of point “P”, configuration 2 (noted parallel configuration) is used. Therefore, it is necessary to find a way to determine on line the point’s “P” position: the voltage Vcom and the current Icom corresponding to this point. Then, the load voltage and current are compared to Vcom and Icom. The PVG then switches onto the appropriate configuration.16
low insulation levels. To simplify the implementation, these characteristics have been subdivided into two intervals and a linear approximation has been used in each interval. The first interval lies between 0 and 300W/m2 of insulation, and the second interval extends beyond 300W/m2. These intervals have been carefully chosen to be valid for any other configuration. Figure 7 also shows that Vcom is significantly affected by the temperature. As T increases, Vcom diminishes linearly. Taking into account the temperature’s effect, the equation is corrected and rewritten as follows:
6. Commutation Point “P” The insulation and temperature are the most important factors which affect the solar cell’s characteristics. Therefore, these would be the main parameters which affect the commutation point’s “P” position. Consequently the voltage and current variation have been calculated for different insulation level and different temperatures using the Newton Raphston method.18,19 Typical results are shown in Figures 6 and 7. The chosen example corresponds to a PVG made of 6 modules allowing switches between series configuration Np Ns = 1 6 and parallel configuration Np Ns = 2 3. The electrical characteristics of each module KYOCERA LA 361 K5120 at 1000W/m2 and 25 °C are as follows: open circuit voltage of 21 V, short circuit current of 3.29 A, series resistance of 0.05 Ω. The current, voltage, and power at the optimum power point are 3.05 A, 16.9 V, and 51 W, respectively. Figure 6 shows that the commutation current varies linearly with insulation and is hardly affected by the temperature. Therefore, it can be described by the following equation: Icom ¼ Ko Es
Vcom ¼ RiEs þ βi þ δið25 - T Þ
ð5Þ
where Ri, βi, and δi are constants relative to each interval and calculated at 25 °C. 7. Description of the Experimental Setup An experimental setup has been considered to test the validity of the method (Figure 8). The control card allows insulation and temperature measurements, yielding values of Vcom or Icom using eqs 4 and 5. If the PVG is in the parallel configuration, then the current flow into the load is measured and compared to Icom. If it is higher, the PVG remains in its actual configuration, otherwise it is reconfigured into the series configuration. However, if the PVG is in the series configuration, then the load’s voltage is measured and compared to Vcom. If it is greater, then the PVG remains in its actual configuration, otherwise it is switched onto the parallel configuration. As a result, the PVG is always switched onto its best configuration for any load and any weather conditions online.15
ð4Þ
where Ko is a constant which depends upon of the module’s number and types. Figure 7 shows the commutation voltage variation Vcom as a function of insulation for different temperatures. As it can be seen, the characteristics are not linear at
8. Results and Discussion Figure 9 shows the experimental results obtained with the described system.15 A variable load has been used to cover a large current and voltage ranges. As it can be seen, the commutation from one configuration to another occurs
(20) http://www.scribd.com/doc/26989996/PV-Performance-Tests-0011.
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Figure 12. Commutation current curves. Figure 10. Parallel and series experimental characteristics I-V Es = 780 W/m2, T = 27 °C.
Figure 12 represents the real current and approximate curves obtained for the same configurations at several solar radiations from 10 to 1000W/m2 at 25 °C. In Figure 12, the approximate curve using eq 4 is called the “approximate curve”. As it can be seen on this figure, the real curves are overlapped on each other whatever the temperature. These curves are also close to the approximate one. The RMSE calculations yield the following results: RMSE = 0.002 A (T = 25 °C); RMSE = 0.007 A (T = -5 °C); RMSE = 0.004 A (T = 50 °C). 9. Conclusions In the present work, it is shown a method for determining the instant of commutation of a PVG configuration to another independently of the load constraint regardless the working conditions, in real time. The simultaneous utilization of Icom and Vcom gives good results. The experimental results validate our proposed method. It is therefore a good tool since it adapts to the change of any parameter (load, insulation, temperature). Moreover, this method is applied to all different loads. The commutation point decides the configuration commutation, to another, by comparing it to the operating point. The goal is to draw best power of the PVG. Thus, one avoids to make recourse to the simulation to each time and to each change of load to calculate the difference between operating powers for the two configurations and to decide the moment of the commutation.
Figure 11. Commutation voltage curves.
exactly on the same predicted point “Pcom” as shown in Figures 9 and 10. It coincides similarly with the point “Pcom” of appropriated experimental parallel configuration characteristics alone and the series one alone (Figure 10). Figure 11 illustrates the voltage commutation real curves (a) and the approximate one (b) for the configurations (Np Ns = 1 6 and 2 3) at solar radiation from 100 to 1000 W/m2 at T = 25 °C. The b curve in Figure 11 uses eq 5. The curves overlap on each other. The root-mean-square error (RMSE) is calculated by a program developed in Matlab. The results obtained are RMSE = 0.014 V at 25 °C. For -5 and 50 °C, the RMSE results are, respectively, 0.054 and 0.090 V.
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