This paper presents a dynamic reconfiguration method for electrical connections in a Series-Parallel connected photovoltaic array under partial shading conditions. It is desirable to extract the maximum energy from the array, but it does not occur in situations where the modules have different points of operation caused by shading. The proposed method is then characterized by the maintenance of the PV array dimensions, that is; no module is removed or added to the array. Furthermore, the control algorithm is based on the Rough Sets Theory, which allows the fast and efficient implementation of a control system, comprising rules that identify the system optimal configuration.
The use of photovoltaic (PV) systems has increased significantly in recent years as a viable alternative to conventional methods of generating electricity. The reduction of transmission and distribution losses and the possibility of injecting energy into the utility power grid are also attractive factors for their utilization.
The efficiency of PV systems is deeply influenced by weather conditions. In many situations, the PV panel can be illuminated in a nonuniform way due to shading caused by clouds, trees, neighbor buildings, and even shadows caused by the modules in the array.
Shading is a common phenomenon that causes severe degradation to the extraction of energy in PV systems [
There are several proposals to reduce the degradation of energy in partially shaded systems [
A different approach lies in systems with microinverters, where each module of the PV array is connected to an inverter with a dedicated MPPT (maximum power point tracking) system [
Recent studies suggest the reconfiguration of the PV array electrical connections. In the reconfiguration system, the PV modules are rearranged dynamically, in order to maximize the output power [
The reconfiguration method depends on the type of connection between the modules. One of the most common topologies is the Series-Parallel (SP) connection. The PV modules in this case are connected in series and the resulting rows are connected in parallel. In an SP matrix, the reconfiguration process is based on the shaded modules combination, where modules with similar irradiance levels must be connected in series and the resulting rows are connected in parallel.
Patnaik et al. [
A similar work [
The removal of shaded modules [
The aforementioned reconfiguration systems [
This paper presents an alternative method for dynamic reconfiguration of the connections in a shaded PV array. The proposed method is characterized by the maintenance of the PV array size; that is, no module is removed or added. Another prominent advantage addressed to the proposal is the use of Rough Sets Theory (RST), which can lead to a fast and efficient algorithm of reconfiguration.
The performance of PV systems is influenced by irradiance and temperature. Therefore, environmental conditions are crucial for power generation.
A common effect in PV systems is the shading, which can be partial or full, consequently reducing the output power of the PV system. The reduction depends on other factors such as the type of arrangement, shade position, and intensity of shading.
The work in [
The reconfiguration method proposed in this paper aims to rearrange the PV array, clustering the shaded modules in the least number of PV array columns.
The rearrangement of shaded modules seems to be a simple and intuitive process. However, depending on the number of modules in the array, this can be a complex task.
In an array with
It is possible to change the position of the modules in an SP array with different ways and
In a permutation, the order of the elements is relevant; for example, sequence ABC is different from sequence CBA. However, from the electrical point of view, the order, in which the PV modules are connected in a series row, does not affect the overall result.
From
Among all configurations of interest, one is the most suitable for a given shading profile. This is defined by the amount and position of shaded modules.
The identification of the PV module condition is obtained from parameter
The number of shaded modules is directly related to the possibility of reconfiguration. In an
Equation (
It is important to notice that there are shapes of shade where nothing can be done. In other words, the rearrangement does not cause the output power to be modified. However, in situations where reconfiguration is suitable, at least one configuration may improve the output power. Thereby, the control system is responsible for identifying the best configuration.
The RST is an extension of the set theory, which focuses on the extraction of intrinsic knowledge from a dataset and the creation of rules that summarize the knowledge in this set. It was originally developed by Pawlak at the beginning of the 1980s [
In order to handle the information, data must be organized in a table called information system (IS). IS is a syntactic representation of knowledge of the objects set, represented by the ordered pair
RST is based on the indiscernibility, which is an equivalence relationship between objects, given a subset of attributes, which allows the partition of universe set
Given the information system
The equivalence class of the relation determined by
Based on indiscernibility, it is possible to reduce the extra attributes, obtaining data reduction. A reduction is a subset
The reduction can be a difficult task depending on the amount of data. It is suitable, therefore, to submit such tables to reduction and simplification procedures. In the simplification process, the unnecessary attributes, duplicated lines, and superfluous values are eliminated. This creates simpler rules that represent the knowledge base of the system, in the same way as the original data.
The manual development of a knowledge base using rough sets is an exhaustive task. Considering this issue, computer programs were developed specifically for this type of application. ROSETTA [
Due to the aforementioned characteristics, RST has been chosen for the implementation of the automatic reconfiguration system.
In order to illustrate the methodology and operation of the proposed reconfiguration system, three photovoltaic arrays are taken as examples.
A
CF.01—the 2 × 2 SP matrix reference configuration.
According to expression (
The arrangements shown in Figure
Equivalent connections in a
According to (
Settings of interest in a
According to (
Among 16 possible shadings, there are situations where, according to the shapes of shade, the module reconfiguration is relevant. For the
The data for the system with four modules are shown in Table
Information System of a
U | A | B | C | D | CF |
---|---|---|---|---|---|
|
0 | 0 | 0 | 0 | CF.01 |
|
0 | 0 | 0 | 1 | CF.01 |
|
0 | 0 | 1 | 0 | CF.01 |
|
0 | 0 | 1 | 1 | CF.01 |
|
0 | 1 | 0 | 0 | CF.01 |
|
0 | 1 | 0 | 1 | CF.02 |
|
0 | 1 | 1 | 0 | CF.03 |
|
1 | 1 | 1 | 1 | CF.01 |
|
1 | 0 | 0 | 0 | CF.01 |
|
1 | 0 | 0 | 1 | CF.03 |
|
1 | 0 | 1 | 0 | CF.02 |
|
1 | 0 | 1 | 1 | CF.01 |
|
1 | 1 | 0 | 0 | CF.01 |
|
1 | 1 | 0 | 1 | CF.01 |
|
1 | 1 | 1 | 0 | CF.01 |
|
1 | 1 | 1 | 1 | CF.01 |
The decision attribute CF is obtained from a routine that relates the condition attributes to the reconfiguration criteria defined in Section
Each line of Table
By using the RST it is possible to obtain the essence of the information and to identify the standard in the data. The data in Table A(0) AND B(0) → CF(01) A(1) AND B(1) → CF(01) C(0) AND D(0) → CF(01) C(1) AND D(1) → CF(01) A(1) AND B(0) AND C(1) AND D(0) → CF(02) A(0) AND B(1) AND C(0) AND D(1) → CF(02) A(1) AND B(0) AND C(0) AND D(1) → CF(03) A(0) AND B(1) AND C(1) AND D(0) → CF(03)
The obtained rules express the logic relationship among the condition attributes (A, B, C, and D) and the decision attribute (CF). After combining the eight rules, one can get the three rules listed next. Each rule is related to one of the configurations presented in Figure (A = B) OR (C = D) → (A = C) AND (B = D) AND (A ≠ B) → (A = D) AND (B = C) AND (A ≠ B) →
With these three rules, it is possible to create an algorithm that defines the best configuration for the photovoltaic array under partial shading conditions. Just one of the rules is enabled at a time and the corresponding configuration must be activated so that the system can have the best energy configuration.
A vertical expansion of the
The conception of IS is analogous. However, as the number of array modules increases, there are some redundancies on the information system. There are cases in which the clustering only occurs in one of the settings of interest, although, in some situations, there is more than one possible setting.
From (
According to (
Settings of interest for a
Part of the information system for the
Part of the Information System of a
U | A | B | C | D | E | F | Q | CF |
---|---|---|---|---|---|---|---|---|
|
0 | 0 | 0 | 0 | 0 | 0 | 0 | CF.01 |
|
0 | 0 | 0 | 0 | 0 | 1 | 1 | CF.01 |
|
0 | 0 | 0 | 0 | 1 | 0 | 1 | CF.01 |
|
0 | 0 | 0 | 0 | 1 | 1 | 2 | CF.01 or CF.02 or CF.05 or CF.10 |
|
0 | 0 | 0 | 1 | 0 | 0 | 0 | CF.01 |
|
0 | 0 | 0 | 1 | 0 | 1 | 2 | CF.01 or CF.03 or CF.06 or CF.09 |
|
0 | 0 | 0 | 1 | 1 | 0 | 2 | CF.01 or CF.04 or CF.07 or CF.08 |
|
0 | 0 | 0 | 1 | 1 | 1 | 3 | CF.01 |
|
0 | 0 | 1 | 0 | 0 | 0 | 1 | CF.1 |
|
0 | 0 | 1 | 0 | 0 | 1 | 2 | CF.02 or CF.03 or CF.07 or CF.11 |
|
0 | 0 | 1 | 0 | 1 | 0 | 2 | CF.02 or CF.04 or CF.06 or CF.09 |
|
|
|
|
|
|
|
|
|
|
1 | 1 | 1 | 1 | 0 | 0 | 4 | CF.01 |
|
1 | 1 | 1 | 1 | 0 | 1 | 5 | CF.01 |
|
1 | 1 | 1 | 1 | 1 | 0 | 5 | CF.01 |
|
1 | 1 | 1 | 1 | 1 | 1 | 6 | CF.01 |
From Table
According to RST, shapes of shade that have more than one configuration of interest, for example, situation 4, are considered as inconsistent. In this case, for the same set of condition attributes, there are different decision attributes. However, in an electric circuit, these situations are redundant, since any setting provides the same result.
The concept and effectiveness of the knowledge reduction process become evident in the
Part of 25 rules is written in a simplified form and listed as follows. ((Q = 0 OR Q = 1 OR Q = 4 OR Q = 5 OR Q = 6) OR (D = 1 AND E = 1 AND F = 1) OR (A = 1 AND B = 1 AND C = 1)) → ((Q = 3) AND ((A = 0 AND B = 0 AND D = 0) OR (A = 1 AND B = 1 AND D = 1))) → ((Q = 3) AND ((A = 0 AND B = 0 AND E = 0) OR (A = 1 AND B = 1 AND E = 1))) → ((Q = 3) AND ((A = 0 AND B = 0 AND F = 0) OR (A = 1 AND B = 1 AND F = 1))) → ((Q = 3) AND ((A = 0 AND C = 0 AND D = 0) OR (A = 1 AND C = 1 AND D = 1))) → ((Q = 3) AND ((A = 0 AND C = 0 AND E = 0) OR (A = 1 AND C = 1 AND E = 1))) → ((Q = 3) AND ((A = 0 AND C = 0 AND F = 0) OR (A = 1 AND C = 1 AND F = 1))) → ((Q = 3) AND ((A = 0 AND D = 0 AND E = 0) OR (A = 1 AND D = 1 AND E = 1))) → ((Q = 3) AND ((A = 0 AND D = 0 AND F = 0) OR (A = 1 AND D = 1 AND F = 1))) → ((Q = 3) AND ((A = 0 AND E = 0 AND F = 0) OR (A = 1 AND E = 1 AND F = 1))) → (E = 1 AND F = 1 AND Q = 2) → (A = 1 AND B = 1 AND Q = 2) → (B = 1 AND F = 1 AND Q = 2) → (A = 1 AND F = 1 AND Q = 2) →
For each one of the 64 different shading possibilities, only one rule is satisfied, which indicates the most suitable configuration of interest.
In cases where there are redundancies (rules 11 to 25), the choice of the best configuration is performed in a second stage of the algorithm, where the previous configuration is evaluated.
The previous information setting is used to achieve the least number of changes in the layout of modules under shading conditions. The definition of optimal configuration in redundant conditions is made based on two criteria: if the previous configuration is one of the optimal configurations: the previous setting is maintained; if the previous configuration is not one of the optimal configurations, it is necessary to choose the setting where the least number of modules is displaced.
The horizontal expansion of the
The procedure for the IS creation and determination of rules is similar to the
Settings of interest for a
With the horizontal expansion, the
Part of the Information System of a
U | A | B | C | D | E | F | Q | CF |
---|---|---|---|---|---|---|---|---|
|
0 | 0 | 0 | 0 | 0 | 0 | 0 | CF.01 |
|
0 | 0 | 0 | 0 | 0 | 1 | 1 | CF.01 |
|
0 | 0 | 0 | 0 | 1 | 0 | 1 | CF.01 |
|
0 | 0 | 0 | 0 | 1 | 1 | 2 | CF.01 or CF.04 or CF.07 |
|
0 | 0 | 0 | 1 | 0 | 0 | 1 | CF.01 |
|
0 | 0 | 0 | 1 | 0 | 1 | 2 | CF.02 or CF.05 or CF.12 |
|
0 | 0 | 0 | 1 | 1 | 0 | 2 | CF.03 or CF.06 or CF.13 |
|
0 | 0 | 0 | 1 | 1 | 1 | 0 | CF.01 or CF.02 or CF.03 or CF.04 or CF.05 or CF.06 or CF.07 or CF.12 or CF.13 |
|
|
|
|
|
|
|
|
|
|
1 | 1 | 1 | 0 | 1 | 0 | 4 | CF.02 or CF.05 or CF.12 |
|
1 | 1 | 1 | 0 | 1 | 1 | 5 | CF.01 |
|
1 | 1 | 1 | 1 | 0 | 0 | 4 | CF.01 or CF.04 or CF.07 |
|
1 | 1 | 1 | 1 | 0 | 1 | 5 | CF.01 |
|
1 | 1 | 1 | 1 | 1 | 0 | 5 | CF.01 |
|
1 | 1 | 1 | 1 | 1 | 1 | 6 | CF.01 |
The rules generated from the IS in Table (Q = 0 OR Q = 1 OR Q = 5 OR Q = 6) → ((E = 1 AND F = 1 AND Q = 2) OR (E = 0 AND F = 0 AND Q = 4)) → ((A = 0 AND B = 0 AND C = 0 AND Q = 3) OR (A = 1 AND B = 1 AND C = 1 AND Q = 3)) → ((A = 0 AND B = 0 AND D = 0 AND Q = 3) OR (A = 1 AND B = 1 AND D = 1 AND Q = 3)) → ((C = 1 AND D = 1 AND Q = 2) OR (C = 0 AND D = 0 AND Q = 4)) → ((A = 0 AND B = 0 AND E = 0 AND Q = 3) OR (A = 1 AND B = 1 AND E = 1 AND Q = 3)) → ((B = 1 AND F = 1 AND Q = 2) OR (B = 0 AND F = 0 AND Q = 4)) → ((B = 1 AND E = 1 AND S = 2) OR (B = 0 AND E = 0 AND S = 4)) → ((A = 0 AND E = 0 AND Q = 4) OR (A = 1 AND E = 1 AND Q = 2)) → ((A = 0 AND F = 0 AND Q = 4) OR (A = 1 AND F = 1 AND Q = 2)) →
In order to evaluate the proposed methodology, the circuits designed in Section
Figure
Simplified circuitry of the reconfiguration system for a
The array consists of four PV modules that simulates the behavior of the KS10 by Kyocera module. Its specifications are presented in Table
KS10 specifications.
Parameters | Value |
---|---|
Maximum Power ( |
10 W |
Short-circuit current ( |
0.62 A |
Open-circuit Voltage ( |
21.5 V |
Maximum Power Current ( |
0.60 A |
Maximum Power Voltage ( |
16.9 V |
Since the output current through each module is proportional to the respective solar irradiance, shading is identified by periodic measurements of the short-circuit current
The DLL block executes an algorithm compiled with DEV C++ software. This algorithm is built from the rules obtained with ROSETTA program as presented in Section
Flowchart of the proposed method.
In the flowchart, the current supplied by each photovoltaic array module is read (
PV systems are usually associated with MPPT systems [
To evaluate the sixteen different shading situations in a single simulation test, the current through each PV module is adjusted. In the following tests, the module current has been reduced by 40% so that shading situations can be emulated.
The curves presented in Figure
Power versus time curve for a
The shading sequence is performed according to Table
The reconfiguration system developed for a
Figure
Power versus time curve for a
The simulation results for the
Power versus time curve for a
Although the
The simulation results for 64 shading situations are seen in Figure
For example, the output power is reduced in the
In order to evaluate the proposed method, a reconfiguration system with four PV modules (
Reconfiguration system.
The implementation of this reconfiguration methodology in photovoltaic systems requires additional circuitry such as sensors, switching, and the control system (hardware and software). Those structures can be seen in the schematic of Figure
The PV array is composed of four KS10 modules (Table
The shading identification is performed by measuring the short-circuit current
After signal conditioning, the parameter specifications are sent to the microprocessor (PSoC—CY8C29466). Then, the switching circuit, which is composed of reed relays (HE721A1210), is triggered.
Partial shading conditions were created with the use of tracing paper, which produce uniform shading, thus filtering the incident radiation [
The PV array is connected to a fixed resistive load, where voltage, current, and output power are measured. During the tests, the module temperature reached 60°C, which consequently reduces the available power.
As discussed in Section
Figure
Experimental results: CF.01-CF.02.
The test shown in Figure
When modules A and C are shaded, the setting of interest is configuration 2. Through reconfiguration, it is possible to increase the output power by about 13.5 W according to Figure
A similar test is performed to verify the system performance when modules B and C are shaded. As expected, the output power increases by 13.3 W after system reconfiguration as seen in Figure
Experimental results: CF.01–CF.03.
Analogous to the previous sections, this test can also be divided into four time intervals as seen in Figure
Experimental results: CF.02-CF.03.
After the measurement period (
As indicated in Section
Experimental results: CF.01-CF.01.
At the beginning, all modules are illuminated and, after
This paper has presented the design of a dynamic reconfiguration system for shaded PV arrays with SP interconnection. The proposed method is characterized by the maintenance of the PV array size; that is, the array dimensions do not change.
The methodology is based in Rough Sets Theory, in which the behavior of the proposed reconfiguration system can be defined by simple logical rules, implemented in a low-coast microcontroller.
The operation of the proposed system has been evaluated through computer simulations and experimental tests, while the obtained results have shown its effectiveness. When compared to an array with static connections, the reconfiguration system provides improved extraction of energy under partial shading conditions.
Thus, reconfiguration provides a significant increase in the output power under different situations. The negative effects of shading in the overall efficiency of the PV system are minimized by the reorganization of the array electrical connections; that is, the shaded PV modules are reconnected in the best possible position, according to the settings of interest.
The authors declare that there is no conflict of interests regarding the publication of this paper.
The authors would like to thank CAPES, CNPq, and FAPEMIG for the financial support for this work.