... the PV modules and their power output is proposed through empirical connection ..... voltaic peak power measuring device (PVPM 1000C40) manufactured by ...
JOURNAL OF PHOTOVOLTAICS CLASS FILES, VOL. 6, NO. 1, JANUARY 2007
1
Maximizing the power output of partially shaded photovoltaic plants through optimization of the interconnections among its modules Luiz Fernando Lavado Villa*, Damien Picault†, Bertrand Raison* Seddik Bacha*, Antoine Labonne*
*G2ELab - Grenoble Electrical Engineering Lab, University of Grenoble, France †La compagnie du Vent - GDF Suez, Montpellier, France
Abstract—Photovoltaic (PV) applications worldwide have reported problems with shading. Passing clouds, the moving shade of a neighbor’s chimney or a nearby tree can completely compromise the power production of such plants despite their size or sophistication. In order to address this issue, this paper makes an exhaustive study of the available interconnections among the modules of a shaded PV field and how they impact power production. As a result, a clear relationship between the interconnections of the PV modules and their power output is proposed through empirical connection laws. Index Terms—Photovoltaic plants, partial shading, module interconnection, plant topologies and PV mismatch
I. Introduction The intensive use of fossil fuels has triggered a worldwide discussion about their effect on the environment. As a consequence the number of photovoltaic (PV) power plants installed all over the world has steadly risen in the past few decades. However, experience has shown that their produced power is usually lower than their expected power [1]. There are many factors that contribute to create this difference such as cable losses, non-optimal inverter efficiency or using PV module from different technologies in the same plant. This lower power output can be refered to as “PV mismatch”, althought there is not a consensus in current literature. The study of PV mismatch has followed two great tendencies for the past few decades. The mismatch due to changes in the physical conditions of the PV modules [2], [3] or to non-uniform shading (also referred to as “partial shading”) across the PV field [4], [5]. Authors from both lines of work have proposed strategies to mitigate PV mismatch, varying from power electronics (PE) applications [6], [7] to inner PV field solutions [5], [8], [9]. This paper studies one type of inner PV field solution: the interconnection schemes among the modules. While other authors have studied specific connections schemes for specific shading scenarios [4], [9], this paper proposes a study of all possible shading scenarios and interconnection schemes for a given PV field.
It points out, for each shading scenario, how to minimize the number of interconnections among the modules, while maximizing power output of the whole PV field. These results, validated by field measurements, allow the definition of connection laws that can be applied to any PV field. II. PV mismatch and its variables Studies in PV mismatch involve many different variables. This section details them and proposes a convenient terminology. A. PV model and plant Figure 1 shows the one-diode model which is used in this work to simulate the PV field.
Figure 1.
The equivalent circuit of a PV module [4]
Equation 1 describes the model [2], [10]. Where Iph is the photocurrent, Rp is the parallel resistance, Rs is the series resistance, I is the output current, V is the output voltage and I0 is the reverse saturation current. I = Iph − I0
(V + I · Rs ) exp −1 Vt
−
V + I · Rs Rp
(1)
The variable Vt is defined by equation 2: Vt =
A · k · Tc q
(2)
Where A is the diode ideality factor, k is the Boltzman’s constant, Tc is the operating temperature of the a PV module and q is the electronic charge. Equation 1 shows that the PV module can be seen as a voltage-controlled current source or inversely. PV plants are assembled to provide voltage and current, thus power, to a certain load. The PV modules are connected in series, forming PV strings that provide
JOURNAL OF PHOTOVOLTAICS CLASS FILES, VOL. 6, NO. 1, JANUARY 2007
2
the necessary voltage. These are connected in parallel to deliver the current of the load [3]. Figure 2 shows an example of a PV plant and its connection to the grid. In this case, the number of modules in one string (M) is 5, and the number of strings (N) is 6.
Figure 4. The visual concept of a connection matrix over a 5x3 PV field [13] Table I The connection matrices of SP, BL, TCT and HC
SP Figure 2.
An example of a 5x6 PV plant
The connection to the grid or the power electronics interface of the PV plant are not in the scope of this work. B. PV pant topologies In this paper, any connection type among the modules of a PV plant is called a topology. The following figure shows four topologies that can be found in the current literature [5], [11].
Figure 3.
The four reference topologies used in this work
The letters below the topologies are the abreviation of their names. SP stands for “series-parallel”, with long strings. BL means “bridge-link”, being inspired on a wheatstone bridge connection. TCT is “totally cross tied”, having all its modules interconnected. And HC is short for “honey comb”, with a pattern similar to the domestic utensil [5], [11]. C. Connection Matrix Throughout the literature, authors have used different topologies, hence connection matrices, to mitigate the mismatch effect in PV plants [2], [5], [6], [8], [10], [12]. Topologies can be mathematically described into a matrix, called connection matrix. It has (M-1) lines and (N-1) columns, representing the possible connections in a PV plant. Figure 4 illustrates these by green squares [13]. The connection matrix is composed of ones and zeros representing its connections and holes, respectively. Table I shows the connection matrices for each of the topologies mentioned above.
0 0 0 0
BL 0 0 0 0
0 1 0 1
TCT 1 0 1 0
1 1 1 1
1 1 1 1
HC 1 0 0 1
0 1 1 0
D. The mismatch effect The mismatch is related to the power losses of a solar cell, module or plant operating under adverse conditions. These include soiling, poorly solded cells, non-uniform irradiation, temperature variations, cell cracking and partial shading [4]. Each one of these can be modeled as a variation on the parameters of the model presented previously. The study of these effects can be split into internal and external mismatch, based on which parameter of the model is affected. The Internal Mismatch can be seen as a variation of the parameters of a PV module due to changes on its physical conditions. These variations can be due to the variability of the cells, common to manufacturing processes. The parameters affected are the series resistance (Rs ), parallel resistance (Rp ), the thermal voltage (Vt ) and the reverse saturation current (I0 ). Detailled explanation of all these parameters, their possible variations and how they are influenced by temperature can be found in [14]. The external mismatch regroups all conditions that lead to a change in the photocurrent (Iph ) of the PV module, such as cell cracking or partial shading. These conditions, explained in detail in [14], lead to a fall in the current production of the cell or module. Thus, the modules operating normally impose their higher current over any shaded module connected in series, forcing these into reverse bias and dissipating power. This effect compromises the power production and the physical integrity of the modules [2], [6], [14]. This paper does not study the internal mismatch. Instead, it focuses its attention in the external mismatch inducting it through the use of artificial shadows. 1) Bypass and blocking diodes: protections against the external mismatch: When a module or cell is in reverse bias, it starts to dissipate power through heat. If nothing is done to protect them, they may suffer a thermal breakdown when reaching high temperatures. The answer
JOURNAL OF PHOTOVOLTAICS CLASS FILES, VOL. 6, NO. 1, JANUARY 2007
M ismatch =
∆P Ptheoretical
(3)
N Width of the shadow
found to protect these modules or cells is to connect bypass diodes in parallel with them. Once their voltage becomes negative, the diode is activated, creating a short circuit for the current to pass [12], [15]. If a bypass diode is active, it changes the number of active cells within a module, reducing its voltage. Thus, other strings or modules connected in parallel may impose a backfeed current which may also threat the bypassed PV module. To avoid this, a blocking diode can be placed in series with each string.[16] The modules of the PV plants simulated and measured during this work are all equiped with bypass diodes, but not with blocking diodes. 2) The mismatch losses indicator: To evaluate the impact of the external mismatch in power production, the mismatch losses performance indicator will be used in this work. It describes how much power has been lost in comparison with the maximum theoretical power available. It can be described by equation 3 [5], [11]:
3
Short & wide
Long & wide
Short & narrow
Long & narrow
Length of the shadow Figure 5.
M
The four different shadow types
It is important to note that in this work, a shadow is considered to be cast upon all cells of a module with the same intensity. 1) The shadow identification code: In order to easily reference any shadow, an identification (ID) code is proposed. This code is based on the number of shaded modules in each string, starting from the positive voltage busbar. Figure 6 shows an example of three shadows and their associated ID codes.
Where the power lost, or ∆P , can be calculated by equation 4 [2]. ∆P = Ptheoretical − Psimulated
(4)
And the maximum theoretical power can be calculated as the sum of all the maximum power of each module, given by equation 5. Ptheoretical =
M ·N X
Pmax (i)
(5)
i=1
Where Pmax (i) is the maximum power of the module i alone, for the given conditions of irradiance, temperature and shadow. E. The characteristics of a shadow The main objective of this work is to estabilish a clear relationship between topologies, shadows and the maximum power point of the PV plant. In order to do so, the characteritics of the simulated shadows must be mathematically modelled. This is done through the use of two characteristics: shading factor and shadow shape. The intensity of a shadow represents how much it can filter the power that shines over the module. This power is called irradiance and it is measured in watts per square meter. In this study the intensity of the shadow will be called shading factor and its value ranges from 0 (no shadow) to 1 (full shadow). No shadow means that the whole available irradiance shines over the module. The shadow shape is described by the number of strings (width) and modules per string (length) that it is cast upon. It can be classified into four different types as represented in figure 5.
Figure 6. Three different shadows, with their respective shadow ID codes
III. Simulation To take into account all the previous variables, the simulations need to be flexible enough to allow changes in the shadow shape, shading factor, connection matrix and parameters of the modules. A software was developed based on the PhD work of Damien Picault and its core ideas are described in [10]. Figure 7 represents the inputs and outputs of the software, called Toposolver. Connection Matrix M and N Psimulated Parameters Toposolver Irradiance Shading factor
Ptheoretical
Shadow shape
Figure 7. The inputs and outputs of the simulation program (Toposolver)
JOURNAL OF PHOTOVOLTAICS CLASS FILES, VOL. 6, NO. 1, JANUARY 2007
Table II The inputs of each simulation setup
Variable name
1st setup
2nd setup
M - Modules/string N - Strings
5 3 SP TCT BL HC Table III W 1000 m 2 Table IV 0.2 to 0.9
3 3 All possible Table III W 1000 m 2 Table IV 0.95
Connection Matrices Module parameters Irradiance Shadow Shapes Shading Factor
Table III The module parameters used in the simulations
Input variable
1st setup
2nd setup
Series Resistance - RS [Ω] Parallel Resistance - RP [Ω] Photocurrent - IP H [A] Reverse saturation current - I0 [A] Foward Voltage - VT [V ]
1.16 999.86 3.83 0.00 2.97
0.4 1000 4.78 0.00 1.6
The photocurrent used in the second simulation setup has a variation of ±0.05%. This is due to the fact that the data were extracted from non-homogeneous PV modules.
In order to minimize the number of simulations, one shadow was chosen for each shadow type, and are detailed in table IV. Table IV The chosen shadow shapes and their ID codes
Shadow Type Short and Narrow Long and Narrow Short and Wide Long and Wide
1st setup
2nd setup
100 400 222 443
100 200 111 332
A. Simulation Results Each figure shows the mismatch losses for different topologies as a function of the shading factor. The simulated shadow can be seen in their upper right corner. 1) First simulation setup - Shadow study: Figure 8 shows that none of the reference topologies can mitigate the external mismatch for short and wide shadow types, no matter the shading factor. 35.00 30.00 25.00
Mismatch Losses (%)
Two simulation setups are used to study the relation between the topologies, the shadows and the maximum power point (MPP) of the PV plant. The first simulation setup, or shadow study, benchmarks the impact of variations in the shading factor and shadow shape over the classical topologies described in section II-B. In order to do so, it uses a 5x3 PV field, which is the minimum size needed to properly reproduce the patterns of the four classical topologies.The shading factors used for the benchmarking vary from 0.2 to 0.9, with steps of 0.1. The module parameters used in this setup were based on a HIP-200BA3 module of Sanyo Energy USA. All modules are considered to be identical. The second simulation setup, or optimization study, explores all available topologies of a given PV field to find out which one maximizes power while minimizing the number of interconnections for specific shadow shapes. Its results will be compared to field measurements performed in a 3x3 PV field available on the rooftop of the french National Superior School of Water, Environment and Energy (EN SE 3 ), located in Grenoble, France. The module parameters for this setup were extracted directly from the modules. The extraction method is described in detail in [9]. A very high shading factor was chosen for this setup because it is easier to reproduce in field measurements. The details for each simulation setup, their respective PV plants size, topologies, shadow shapes and model parameters are summed up in Tables II and III.
4
20.00 15.00 SP TCT BL HC
10.00 5.00 0.00 0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
Shading Factor
Figure 8.
Simulation results for the short and wide shadow type
There is a significant reduction in mismatch losses for higher shading factors. As shading factor raises, the power available in the bypassed modules represents a smaller share of the total theoretical power. And since the mismatch losses were defined as a ratio between the power produced by unshaded modules and total theoretical power (equation 3), the ratio simply diminishes. Figure 9 shows that all four topologies have virtually the same performance when most of the modules are shaded. This implies that once the shadow is spread over most of the PV field, the topologies are no longer a viable solution to the external mismatch problem, no matter the shading factor. Figure 10 shows that for short and narrow shadows, changing the topology is an interesting solution to mitigate the external mismatch, depending on the shading factor. In this case, the TCT topology is most effective agaist mismatch losses for low shading factors, while SP minimizes mismatch losses for higher shading factors.
JOURNAL OF PHOTOVOLTAICS CLASS FILES, VOL. 6, NO. 1, JANUARY 2007
5
N
60.00
40.00
30.00 SP BL HC TCT
20.00
10.00
0.00 0.2
0.3
0.4
0.5
0.6
0.7
0.8
Width of the shadow
Mismatch Losses (%)
50.00
Short & wide No topology is effective
Short & narrow TCT for low SF SP for high SF
Length of the shadow
Figure 12. The shadow types and their respective most effective topologies for the first simulation set
16.00 14.00
Mismatch Losses (%)
M
Simulation results for the long and wide shadow type 18.00
12.00 10.00 8.00 6.00
SP BL HC TCT
4.00 2.00 0.00 0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
2) Second simulation setup - Optimization Study: In this simulation group, the results are also displayed according to their shadow type. At each figure, the simulated MPPs of all possible topologies of a 3x3 PV field will be plotted. The simulated shadow is displayed on the left. Figure 13 shows that the difference between the best connection matrix and the worse is less than 1 W. This confirms that there is no topology that can reduce mismatch losses for short and wide shadows, as seen in the first simulation setup.
Shading Factor
756.20
Figure 10. Simulation results for the short and narrow shadow type
756.10 756.00
Maximum Power Point (W)
Figure 11 shows that the TCT is the topology with the best performance for long and narrow shadows, no matter the shading factor. It also shows that SP is less interesting, which indicates that the connections among the modules have a direct impact over power production in this case. 8.00
755.90 755.80 755.70 755.60 755.50 755.40 755.30
7.00
755.20 6.00
Mismatch Losses (%)
Long & narrow TCT for all SF
0.9
Shading Factor
Figure 9.
Long & wide No topology is effective
Connection Matrix
5.00
Figure 13.
4.00 3.00
SP BL HC TCT
2.00
MPP values for the short and wide shadow type
Figure 14 shows that the optimal topology is 1100. The power production is mostly affected by connections on the higher part of the PV plant. 101.00
1.00 0.00 0.2
00 00 00 00 01 01 01 01 10 10 10 10 11 11 11 11 00 01 10 11 00 01 10 11 00 01 10 11 00 01 10 11
0.3
0.4
0.5
0.6
0.7
0.8
100.00
0.9
Figure 11.
Maximum Power Point (W)
Shading Factor
Simulation results for the long and narrow shadow type
The conclusions of these analyses are summed up in figure 12. These results confirm that topologies can have a direct impact in power production, depending on the shadow type and the shading factor. It is also clear that the TCT topology might be the best solution to mitigate external mismatch for most of the shadow types. However, could it be possible that some connections might be redundant and could be eliminated without loss of power? The second simulation setup will be used to investigate this question.
99.00
98.00
97.00
96.00
95.00
00 00 00 00 01 01 01 01 10 10 10 10 11 11 11 11 00 01 10 11 00 01 10 11 00 01 10 11 00 01 10 11 Connection Matrix
Figure 14.
MPP values for the long and wide shadow type
Figure 15 shows that any topology sharing the first two connections (11XX), hence connecting the shaded to the unshaded part of the module, has a good performance.
JOURNAL OF PHOTOVOLTAICS CLASS FILES, VOL. 6, NO. 1, JANUARY 2007
6
940.00
IV. Measurements
930.00
Maximum Power Point (W)
920.00 910.00 900.00 890.00 880.00 870.00 860.00
00 00 00 00 01 01 01 01 10 10 10 10 11 11 11 11 00 01 10 11 00 01 10 11 00 01 10 11 00 01 10 11 Connection Matrix
Figure 15.
MPP values for the short and narrow shadow type
Figure 16 shows that only topologies based on XX11 have an effect on the maximum power point. All of these topologies connect the shaded string with the unshaded strings. 900.00 895.00
Field measurements were conducted in order to validate the conclusions from both simulation setups. The field data is composed of I-V curves measured with a photovoltaic peak power measuring device (PVPM 1000C40) manufactured by Photovoltaik Engineering Company. The measurement method is described in detail in [17]. The PV field is composed of a 9 Photowatt PW1650 modules, in a 35° tilt angle, installed at the rooftop of the ENSE3 in Grenoble, France. The modules were connected into a 3x3 field and covered with cardboard paper, reproducing the same six shadow shapes and the high shading factor chosen previously. The measurements were carried out between 10h30 and 13h30, sun time, from July 22nd to 25th of 2010. Four connection matrices were chosen to be measured with each shadow scenario. They are represented in figure 18.
Maximum Power Point (W)
890.00 885.00 880.00 875.00 870.00 865.00 860.00
00 00 00 00 01 01 01 01 10 10 10 10 11 11 11 11 00 01 10 11 00 01 10 11 00 01 10 11 00 01 10 11 Connection Matix
Figure 16.
MPP values for the long and narrow shadow type
Figure 17 sums up the conclusions from this simulation set.
Width of the shadow
N
Figure 18. 1111
The chosen connection matrices: 0000, 0011, 1100 and
The measurements were made under similar irradiation and temperature, which are detailed in table V. A. Results and discussion
Short & wide No topology is effective
Short & narrow Optimal Topologies: 11XX
Long & wide Optimal Topology: 1100 Long & narrow Optimal Topologies: XX11
Length of the shadow
M
The results of the measurements are displayed according to the shadow type. The figures display curves of the power of the PV plant as a function of its voltage, called P-V curves. Each measured curve is compared to its equivalent simulation curve. The shadow shape is represented on the upper right corner of the measured P-V curves. 1) The Short and Wide shadow: Figure 19 confirms that none of the studied topologies have any influence over the power output. All topologies have the same PxV curve. 800
Figure 17. The shadow types and their respective optimal topologies for the second simulation set
700 600 500 Power (W)
The observations from the second simulation setup can be summed up in the the following connection laws: 1) The connections should be done at the frontier between shaded and unshaded modules. 2) Beyond a certain shadow size, the topologies have little or no effect over the external mismatch. 3) There is an optimal topology and any topology containing it will also have a very good performance. 4) The optimal topology is dependent of the shadow scenario. To confirm these laws, some key results will be compared to field measurements.
400
0000 1100
300
0011 1111
200 100 0 0
Figure 19.
20
40
60 Voltage (V)
80
The simulated P-V curve
100
JOURNAL OF PHOTOVOLTAICS CLASS FILES, VOL. 6, NO. 1, JANUARY 2007
7
Table V The environmental conditions during the measurements Shadow type
Shadow code
Short and Narrow Long and Narrow Short and Wide Long and Wide
100 200 111 332
Module Temp.(℃) 44.7 46.2 45.1 46.1
Environment Temp. (℃)
±8% ±7% ±8% ±5%
34.7 35.0 35.2 35.8
The measurements results are represented in figure 20. The power output of the PV field with the SP and TCT topologies are similar, close to maximum and higher than the power output of the other topologies.
978 ±0.02% 1017 ±0.04% 1002 ±0.06% 1020 ±0.03%
±2% ±1% ±2% ±2%
100 90 80
800
70
Power (W)
700 600 500
Power (W)
W Irradiance ( m 2)
60 50 40 0000 1100 0011 1111
30
400
20
300
10
0000 1100 0011 1111
200
0
0
20
40
60
80
100
Voltage (V)
100
Figure 22. 0
20
40
60
80
100
Voltage (V)
Figure 20.
The measured P-V curve
The power variations can be explained by changes in irradiation and temperature conditions during measurements. It is also possible to note a difference in the power output between the two figures for voltages higher than approximatly 70 V. This is due to the slight difference between the shading factor of the simulation (0.95) and of the measurement (1). They are different because the simulation software has problems converging for shading factors higher than 0.95. 2) The Long and Wide shadow: Figure 21 shows the simulation results for this shadow type, with the optimal topology being 1100.
The measured P-V curve
They confirm 1100 as the optimal topology, but the power output of the PV field is almost identical for all measured topologies. The difference in the power output for voltages higher than approximately 30 V are also due to the difference in shading factor of the simulation (0.95) and the measurement (1). 3) The Short and Narrow shadow: Figure 23 shows that the topology which maximizes power output and minimizes the number of connections is 1100. 1000 900 800 700 Power (W)
0
600 500
0000 1100
400
0011 1111
100 300 90 200 80 100
Power (W)
70 0 0
60
0000 1100 0011 1111
50 40 30 20 10 0 0
Figure 21.
20
40 60 Voltage (V)
80
100
The simulated P-V curve
The measurements results are represented in figure 22.
Figure 23.
20
40
60 Voltage (V)
80
100
120
The simulated P-V curve
The results in figure 24 confirm that the power output of the PV field with the connection 1100 is similar to 1111, and close to maximal. These slight differences can be explained by a change in temperature and available irradiance. These results confirm that the connections can have an important impact in power production in a PV plant.
JOURNAL OF PHOTOVOLTAICS CLASS FILES, VOL. 6, NO. 1, JANUARY 2007
1000 900 800
Power (W)
700 600 500 400 0000 1100 0011 1111
300 200 100 0
0
20
40
60
80
100
120
Voltage (V)
Figure 24.
The measured P-V curve
8
An optimal topology creates an alternative path that best redistributes current among shaded and unshaded modules using the minimum amount of interconnections. This allows the PV modules to work, even if under adverse conditions, as close as possible to their individual maximum power point. Hence, the PV field can globally produce more power. Shadows which cover all strings or most of the surface of a PV field severely compromise its capability of rerouting the produced current. This explains why topologies are not an answer for these shadow types. This idea can be graphically expressed by the figure below. Here, a hypothetical PV field is partially shaded and has an optimal interconnection scheme, as shown in figure 27.
4) The Long and Narrow shadow: Figure 25 shows an equivalent performance between the 1111 and 0011 topologies. 900 800 700
Power (W)
600 500
0000
400
1100 0011 1111
300
100
Figure 25.
20
40
60 Voltage (V)
80
100
A hypothetical optimal topology
The distribution of current is detailed in figure 28. All of the modules are working with different currents, which could be seen as the local optimal power points. This means that the hypothetical optimal topology allows the produced current to find the optimum path among all modules of the field.
200
0 0
Figure 27.
120
The simulated P-V curve
The measurements results in figure 26 confirm that the power output of the PV field with the topologies 1111 and 0011 are similar and close to maximal, despite variations in temperature and irradiance. 900 800 700
Power (W)
600 500
Figure 28. 400 0000 1100 0011 1111
300 200 100 0
0
20
40
60
80
100
120
Voltage (V)
Figure 26.
The measured P-V curve
These results validate that the important connections for maximizing power are those located at the frontier between the shaded and unshaded modules. 5) Discussion on the simulation results: Based on these results, the following definition can be proposed:
The effects in the distribution of currents
It is important to note that this is but an abstraction, yet to be confirmed throught simulation and measurement. V. Conclusions This paper has investigated how a change in the interconnections among the modules within a shaded PV field can impact its maximum power point. The work has been done in three parts. The first was a shadow study, where simulations were made using certain fixed interconnection schemes while varing the shadow. Following was the optimization study, where certain shadows remained fixed while the interconnections were allowed to vary.
JOURNAL OF PHOTOVOLTAICS CLASS FILES, VOL. 6, NO. 1, JANUARY 2007
From these simulations, four shadows and four interconnection schemes were chosen for measurements in a real PV field, located on the rooftop of the ENSEÂş, in Grenoble, France. The measurements were compared with the simulations and the conclusions were summed up in the following connection laws: 1) The connections should be done at the frontier between shaded and unshaded modules. 2) Unshaded modules should be connected to each other in order to create escape routes for the surplus current. 3) Shaded modules should also be connected to each other, allowing them to redistribute their current and work at their local maximum power point. These connection laws are only valid for 3x3 PV fields, and their generalization for any field of any size is still under research. However, they can be used as guidelines for conceiving algorithms that seek the optimum power production of any PV field under dynamic shading. Two definitions were also proposed as theoretical conclusions to this paper: 1) A topology is as a set of alternative paths for the produced current to flow within of a PV field. 2) An optimal topology is the one that, for a given shadow, uses the minimum number of interconnections to create a current redistribution path that brings all modules as close as possible of their local maximum power points. These two definitions imply that topologies can only be used as a solution for partial shading if the shadow shape spares a path that allows the rerouting of the produced current. Acknowledgments The authors would like to thank the french National Institute of Solar Energy (INES) for provinding the I-V tracer which was used during our measurements. We also extend our thanks to the EN SE 3 for allowing us to use its PV field for our measurements. References [1] M. Sadok and A. Mehdaoui, “Outdoor testing of photovoltaic arrays in the saharan region,” Renewable Energy, vol. 33, no. 12, pp. 2516 – 2524, 2008. [2] N. Kaushika and A. K. Rai, “An investigation of mismatch losses in solar photovoltaic cell networks,” Energy, vol. 32, no. 5, pp. 755–759, 2007. [3] J. Appelbaum, A. Chait, and D. A. Thompson, “A method for screening solar cells,” Solid-State Electronics, vol. 38, no. 1, pp. 246–248, 1995. [4] E. Karatepe, M. Boztepe, and M. Çolak, “Development of a suitable model for characterizing photovoltaic arrays with shaded solar cells,” Solar Energy, vol. 81, no. 8, pp. 977–992, 2007.
9
[5] N. D. Kaushika and N. K. Gautam, “Energy yield simulations of interconnected solar pv arrays,” Power Engineering Society General Meeting, 2003. [6] N. H. B. Prasad Koirala, B. Sahan, “Study on mpp mismatch losses in photovoltaic applications,” 24th European Photovoltaic Solar Energy Conference and Exhibition, 2009. [7] G. C. Arnett, J.C., “Photovoltaic module hot spot durability design and test methods,” p. 1099âĂŞ1105, Proceedings of the 15th IEEE Photovoltaic Specialists Conference, 1981. [8] J. Dobon, F. Lugo, A. Valera, P. Osuna, R. Acosta, L. Marichal, and G. Monedero, “Numerical simulation of current-voltage characteristics of photovoltaic systems with shaded solar cells,” Photovoltaic Energy Conversion, 2003. Proceedings of 3rd World Conference on, vol. 2, pp. 2043–2045, 2003. [9] D. Picault, B. Raison, S. Bacha, J. de la Casa, and J. Aguilera, “Changing photovoltaic array interconnections to reduce mismatch losses: a case study,” p. 37, 9th International Conference on Environment and Electrical Engineering (EEEIC), 2010. [10] D. Picault, B. Raison, S. Bacha, J. de la Casa, and J. Aguilera, “Forecasting photovoltaic array power production subject to mismatch losses,” Solar Energy, vol. 84, no. 7, pp. 1301 – 1309, 2010. [11] Y.-J. Wang and P.-C. Hsu, “Analysis of partially shaded pv modules using piecewise linear parallel branches model,” World Academy of Science, Engineering and Technology, no. 60, 2009. [12] A. Woyte, J. Nijs, and R. Belmans, “Partial shadowing of photovoltaic arrays with different system configurations: literature review and field test results,” Solar Energy, vol. 74, no. 3, pp. 217–233, 2003. [13] D. Picault, Reduction of mismatch losses in gridconnected photovoltaic systems using alternative topologies. Phd thesis, Institut National Polytechnique de Grenoble - INPG, Oct. 2010. [14] E. van Dyk and E. Meyer, “Assessing the reliability and degradation of photovoltaic module performance parameters,” IEEE Transactions on reliability, vol. 53, pp. 83–92, March 2004. [15] V. Quaschning and R. Hanitsch, “Numerical simulation of current-voltage characteristics of photovoltaic systems with shaded solar cells,” Solar Energy, vol. 56, no. 6, pp. 513–520, 1996. [16] B. Lehman, J. de Palma, J. Mosesian, Y. Zhao, and R. Lyons, “Challenges to overcurrent protection devices under line-line faults in solar photovoltaic arrays,” Energy Conversion Congress and Exposition (ECCE), 2011. [17] A. Wagner, “Peak-power and internal series resistance measurement under natural ambient conditions,” EuroSun-Copenhagen, 2000.
