1. Introduction
Solar energy is one of the renewable energy sources and it has been used extensively in solar power generation systems [
1]. Photovoltaic (PV) modules are the main components of these systems and they are non-linear direct current (DC) power sources. The available power of the modules depends on the amount and distribution of solar irradiance. If the entire surface of a module is exposed to the same solar irradiance, its P-V curve only has a single maximum power point (MPP). This can be defined as a uniform irradiance condition (UIC). In that kind of a condition, maximum power point tracking (MPPT) can be accomplished by conventional algorithms, such as perturb and observe (P&O) [
2], incremental conductance (IC) [
3], fractional short circuit current (SCC) [
4], and fractional open circuit voltage (OCV) algorithms in this condition [
5]. However, in a roof type and/or building integrated PV (BIPV) system, they probably do not extract maximum power in partial shading conditions (PSCs) due to the complexity of P-V curves and/or wrong decision when the first MPP is reached. Therefore, several algorithms and methods have been proposed in order to realize global MPPT (GMPPT [
6,
7,
8,
9,
10,
11,
12,
13,
14,
15,
16,
17,
18,
19,
20,
21,
22,
23,
24,
25,
26,
27,
28].
Studies in literature that were conducted for GMPPT can be divided into two groups. General feature of the first group is based on the characteristic curves of PV modules. A two stage MPPT control algorithm that is based on instant measurement of OCV and SCC of PV module is proposed in [
6]. In the first stage, the vicinity of GMPP is aimed to be reached by using the load line approach. The derivative of power with respect to voltage is used in the second stage, afterwards. A similar strategy has been proposed in [
7]. Tey et al. proposed a 0.8 V
OC model that was based on the GMPPT technique with a modified IC algorithm. Even if it shows satisfactory performance, the tracking speed is small due to the HC strategy in the first stage of their algorithm. Fibonacci search algorithm is used for tracking GMPP in a PV system in [
8]. An MPPT algorithm that is based on PV characteristics has been developed by conducting extensive simulation studies in [
9]. Dividing rectangles (DIRECT) algorithm has been used in another study for searching the GMPP by defining a P-V curve as a Lipschitz function [
10]. The area dividing strategy and potentially optimal interval for tracking parameters are defined by using PV parameters, which results in high system dependency. A voltage scanning based MPPT approach that operates on the load characteristic curve is implemented. It is claimed that the voltage value at MPP is higher than a reference value that is set by the authors in [
11]. According to Ji et al., when PSC is detected, vicinity of GMPP can be easily tracked by using a linear function [
12]. However, some coefficients have to be calculated, so as to detect PSC, which increases the system dependency of this study. A PV characteristic that is based on the MPPT algorithm has been proposed in [
13]. An analytical condition is introduced for PSC detection in this study, but there is a disadvantage for this algorithm in that it is highly system dependent.
The algorithm used in [
14] takes the number of bypass diodes and possible voltage bands that appeared in the P-V curve into consideration. Voltage band is to be determined for GMPPT. This power is estimated by polynomial fitting obtained from a few voltage samples taken for certain conditions in [
15]. A complete scanning is avoided in this way. A field programmable gate array (FPGA) based MPPT method that uses a charging of the capacitor connected to the output of PV module is used. The voltage and current of capacitor are stored and GMPP is determined during the charging. Independence of the system parameters and configuration types are the prominent feature of this approach. However, the periodical charging of this capacitor leads to a disconnection between the PV array and load [
16]. The segmentation search method based on PV characteristics [
17], working mechanism of bypass diodes [
18], and an algorithm using the relationship between load line and I-V curve with trigonometric rule is presented to increase response time under changing environmental and load conditions [
19]. On the other hand, in another group of studies, some novel methods, like artificial neural network (ANN) [
20], fuzzy logic [
21], particle swarm optimization (PSO) [
22], differential evolution algorithm [
23], and full scanning based and evolutionary algorithms (such as ant colony optimization and genetic algorithm) have been proposed in [
24,
25,
26,
27,
28].
A smart PV module approach has been very popular, especially in a small PV system, since it performs its own MPPT and a high tracking efficiency is obtained [
23,
28]. It will be not surprising that MPPT can be panel dependent in the future. Tracking efficiencies and tracking speed decreases in PSC, which results in the unreliable operation in PV systems. To prevent this unreliable situation, a novel GMPPT algorithm that is based on PV characteristics and duty ratio initialization is proposed for micro converter/DC power optimizer applications in this paper. Partial shading deciding approach to determine the correct MPP region on the P-V curve is provided by measuring included bypass diode voltages in a module. This approach employs some duty ratios that are calculated by extensive simulations carried out for the P-V curves of the PV modules. As known, this approach is feasible for micro converters, since a PV module has limited bypass diodes included. A single ended primary inductance converter (SEPIC) is used as the power processing unit in order to validate the performance of the proposed algorithm. The remains of this paper continue, as follows: The current-voltage (I-V) and P-V curves of typical PV modules for UIC and PSCs are described in
Section 2. Furthermore, the operation of the bypass diodes in a module is explained in this section. The proposed algorithm is extensively explained in
Section 3. The results of the simulation and experimental studies that verify the proposed methodology are released in
Section 4 and
Section 5, respectively. The contributions of this study are highlighted as conclusions in the last section.
2. PV Characteristic in PSC
The smallest piece of PV modules is a solar cell, whose power depends on the value of solar irradiance and temperature. Solar cells are connected in series to each other, forming modules that have exponential I-V and P-V characteristics under UICs. There is only single MPP on the I-V curve in this condition as presented in
Figure 1a. If a module is exposed to a PSC and if there are no bypass diodes included, it generates power depending on the intensity of shadowing, which substantially reduces the available power, as presented in
Figure 1b. In this condition, partially shaded solar cells behave as a load and consume some energy, instead of generating [
12]. If the amount of the energy consumed increases much, it is possible that a hotspot problem occurs and PV modules are destroyed because of excessive thermal stresses. Therefore, bypass diodes are used for protecting modules. A number of these diodes are generally determined by the rated power of the modules. Generally, PV modules do not have more than three bypass diodes, except for any specific products [
29]. In
Figure 1 c, the module has three bypass diodes, which may lead to three MPPs on the P-V curve. The maximum power is bigger for the case with bypass diodes than that for the case without them, as shown in
Figure 1b. Furthermore, the P-V curve becomes more complex than the one under UICs.
When a PSC occurs, the I-V curve of a PV module becomes similar to a ladder, as shown in
Figure 2. For example, a module has three series connected cell groups and all of the groups have their own bypass diodes. I-V curve of this module is given in
Figure 2. It is seen that one of the shaded cell groups of the module starts to generate power, when current of the module is equal to the one of the shaded cell groups (PV-2). First, PV-1, which is the highest irradiated cell group, generates power alone until the current of PV-2 becomes equal to a current of the module, as shown in
Figure 2. The voltage of PV-2 is negative and it behaves as a load before it starts to generate power. It is worth noting that, when shaded part of the module starts to generate power, its voltage gets positive value. That is, in each stair of the ladder, the voltage of PV module increases, since each cell group starts to generate power one by one, as presented in
Figure 2.
Partial shading is the most problematic condition for PV modules, which not only reduces the available power of the modules, but also increases the complexity of P-V and I-V curve of them. In other words, partial shading causes an increment in the number of MPPs on the P-V curve, which makes MPPT difficult when compared with the complexity level of UICs. Besides that, HC algorithms may not able to find GMPP [
9], since they stop tracking when the first MPP is tracked. However, the exact maximum power may not be this one. The entire P-V curve should be scanned in order to find the GMPP by using these algorithms. However, convergence time increases, deteriorating MPPT quality. In the proposed methodology, a new duty ratio initialization based algorithm is introduced with the help of the general characteristics of PV modules.
3. Materials and Methodology
Researchers have developed GMPPT algorithms by proposing a mathematical equation or defining an index before, so as to detect PSC [
7,
8,
9,
10]. Generally, they define an equation and check it in a certain time interval. Subsequently, a PSC block starts to be operated for finding the vicinity of MPP correctly. Most of them use an HC based algorithm, finally. The main drawbacks of these studies are the increase in stage numbers, computational burden, dependency of system parameters, and inclusion of different algorithms for uniform irradiance and PSCs. On the other hand, in this study, significant clues in characteristic curves of PV modules are employed in the context of the proposed GMPPT algorithm, which is explained in the next sections.
In recent years, hardware based approaches have been aimed to be developed, even if MPPT is mostly accepted as a software based operation. In a classical PV system, a centralized power converter unit makes the conversion and controlling of entire power. For example, there are several PV modules connected in series and/or parallel, forming a PV array. This array is connected to a centralized converter. Although this type of system has some advantages in terms of ease of implementation and cost, the available power might not be extracted in some cases, like shading and/or malfunction of a part of the system, which leads to decrease the unreliability of such these systems. On the other hand, the micro converter structure introduces new advantages, such as high reliability as compared with the centralized one, high efficiency, easy maintenance options, and ease of MPPT algorithm, which is the main focus of this study. A PV system is given in
Figure 3; all PV modules operate independently and they have their own micro converters that supply to the load/grid/battery. The manufacturing of the junction boxes and PV modules are commercially independent from each other. Most of the time, junction boxes have three bypass diodes that led to three potential MPP regions to track. Since the performance of the proposed algorithm depends on the number of bypass diodes and the micro converter structure requires one module, it means that the proposed GMPPT algorithm is suitable in micro converter applications.
3.1. Preliminary Analyses for Power-Voltage Curve under PSCs
PV modules have multiple MPPs when they are exposed to different solar irradiance. The maximum value of the number of MPPs is equal to the number of bypass diodes in a module. Assume that a module has three series connected cell groups that have their own bypass diodes. Several shading scenarios are generated for simulations in order to characterize P-V curves of a module. In order to determine the number of shading scenarios, the increment of solar irradiance, ∆Q
INC, is set. This parameter can be accepted as 100 W/m
2. Value of solar irradiance varies from 100 W/m
2 to 1000 W/m
2 [
30]. The number of shading cases is calculated for the maximum number of MPPs, as in (1).
In (1), c is the number of shadowing conditions, m is the ratio of the maximum irradiance value and the increment of solar irradiance (m = 1000 W/m
2/100 W/m
2 = 10), and n is the number of bypass diodes in a module. Assume that a module combined with three bypass diodes can receive three different solar irradiances. Thus, there are three MPP regions on the P-V curve as a result. In all of the shading cases, the P-V curves of the module are presented in
Figure 4. It is clear that MPPs are clustered in certain MPP regions. These regions are always vicinity of 80% of the OCV of each cell group [
9,
10,
13,
22]. The proposed algorithm aims to firstly reach the vicinity of the correct MPP region. So as to decide to this region and not to diverge to local MPP, average the equivalent resistance (ER) of the PV module/array at MPP is calculated, as in (2), for the purpose of providing proper duty ratio initialization.
where R
PVavg is the average ER of PV module and V
mpp and I
mpp in (2) are the voltage and current of the module at MPP, respectively. P
mpp is the maximum power value of the module. According to the shading conditions, average ERs of PV module at all MPPs regions are calculated. Subsequently, the values of duty ratios are calculated for them, as given in (3), for a buck-boost converter topology [
31].
R
load is the value of load resistance. D is the duty ratio of the pulse width modulation signal. After the calculation of the duty ratios, necessary analyzes for the searching of the GMPP process is completed.
Figure 5 shows the two P-V curves for the shading with maximum irradiance (minimum R
PV) and minimum irradiance (maximum R
PV) conditions. With the help of an average value of the duty ratio calculated for one MPP region, it is guaranteed that the operating point of a PV module stays in the rectangles that are given in
Figure 5.
3.2. Duty Ratio and Load Characteristic
It is important to know the variation of the duty ratio interval and the value of load resistance in the proposed approach. The value of this interval should be analyzed, so as to prove the effectiveness of the proposed algorithm. It is clear that, for buck-boost converter topology, maximum value of the duty ratio range is roughly 40%, as can be seen in
Figure 6. Although this range increases by a specific value of load resistance, it slightly decreases from this value of resistance. If entire of the P-V curve is scanned normally, duty ratio has to be varied from 0% to 100%, theoretically. However, investigating the variations of duty ratio by load resistance value provides a limited region of duty ratio. Therefore, searching of GMPP becomes easier than entire of the P-V curve scanning. On the other hand, the value of duty ratio changes by the value of load resistance, which should be calculated, before MPPT starts.
Figure 6 shows the relationship between duty ratio and value of load resistance. In this figure, three curves represent the duty ratio variations for three MPP regions. These relationships are obtained by using (3) explained in the previous subsection.
3.3. Proposed Algorithm
This novel GMPPT algorithm is developed by using the I-V and P-V characteristics of a PV module and the simple calculations that are explained before. An electrical circuit of the proposed MPPT system that consists of SEPIC, sensing circuits (voltage divider and current transducer), some electronic components for PSC detection, and MPPT block are presented in
Figure 7. The first consideration is to check whether PV module receives different irradiances or not in this algorithm. In order to decide PSC, NPN type transistors, T
1, T
2, and T
3 are switched on by the MPPT controller. Subsequently, the value of V
d1, V
d2, and V
d3 are evaluated in the control unit. In a PSC, the bypass diodes of the shaded cell groups have negative voltages at the beginning of the I-V curve, as presented in
Figure 2 (illustrated in P1 circle). This can be formulated, as in (4).
I
SC is the SCC of the PV module, Vn is the voltage of maximum irradiated cell groups and the other voltages (V
d1, V
d2, ..., V
dn−1) correspond to the voltage of the partially shaded cell groups, here. In order to satisfy (4), the value of duty ratio should be as much as big. In this condition, the current of PV module is roughly equal to SCC (I
PV ≈ I
SC). For a SEPIC, the ER of the PV module can be written, as in (5) [
30,
32].
If the current of the module is roughly equal to the SCC (I
PV ≈ I
SC), the voltage of PV modules is approximately zero. When the ratio of the voltage of the module and current of it is used instead of ER of PV module in (5), the formulation shown in (6) is obtained.
Theoretically, if the duty ratio equals to one (100%), (6) becomes mathematically zero. Therefore, the maximum value of the duty ratio is set to a maximum value (80–90% of duty ratio). For this value of duty ratio, the voltage of a PV module is roughly zero. As presented in
Figure 8a, the voltages of the bypass diodes are checked, so as to determine PSC. If one of the bypass diodes has negative voltage, the duty ratios values are set as d
1, d
2, and d
3 for three MPP regions. The P-V curves of PV-1, PV-2, and PV-3 are scanned by operating all the micro converters with a duty ratio of d
1, d
2, and d
3. As illustrated in
Figure 8b, for each duty ratios, the power of the module is calculated by using the voltage and current of it in each sample time. The maximum value of the power is stored (P
1m for d
1, P
2m for d
2, and P
3m for d
3) as a result of artificial scanning of power, for three MPP regions. Afterwards, the stage of power-duty (P-D) conversion starts. In fact, this stage contains a basic power comparison in order to set the initial value of duty ratio, which corresponds to the maximum power calculated. It is initiated for reaching the vicinity of the GMPP. Finally, P&O algorithm is used. When P&O starts, power change (p) is continuously checked. If this change is bigger than the threshold value of power (p
thr), which should be calculated by the step size of duty ratio value and its corresponding power change, PSC is checked again and the algorithm steps shown in
Figure 8a are operated. If PSC does not occur, it may mean changes in irradiance or the value of load resistance. However, since this study focuses the PSC and its difficulties in GMPPT, this is not taken into consideration in this study.
5. Conclusions
Due to the nonlinear characteristics of PV modules and the PSC, extracting maximum power from them becomes complex and difficult for MPPT systems. In this study, a novel micro converter based GMPPT algorithm, which uses some calculated duty ratios in certain and limited interval, is introduced by using the relationship between ER of PV module and the load value.
Simulation and experimental results show that proposed algorithm manages the tracking GMPP under PSCs. The novelties, contributions, and limitations of this algorithm can be summarized, as follows:
Voltage values of the bypass diodes are checked in order to detect partial shading. If one of the bypass diodes has a negative voltage value, it can be understood that partial shading occurs. However, the voltages of bypass diodes have to be measured under a specified condition. If the maximum value of duty ratio is set to its maximum value, the current of the module is equal to SCC of the module that satisfies the specified condition. It is also worth noting that there is no need to know the SCC of the module.
A contribution presented is about the determination the maximum available duty range in a buck-boost converter topology. It is shown that GMPPs are clustered in a limited duty ratio interval. This interval is approximately 40% for buck-boost converter topology. However, the proposed algorithm does not use a classical scanning procedure. It uses the duties ratios calculated, which are in this limited interval, so as to reach the vicinity of the GMPP. As maximum power is stored for each duty ratios MPP (for all MPPs), it is guaranteed to track GMPP for all shading cases.
The proposed algorithm has low system dependency and it realizes a fast tracking when compared with the compared studies, which is verified by different simulation and experiments.
It is verified by the simulation and experimental studies that the proposed algorithm can be used instead of P&O algorithm with a variable step size approach.
The proposed algorithm is very simple and it leads to the low computational burden. Thus, it can be implemented by a low cost microcontroller. It is expected to have good performance in module based DC power optimizers (micro converter), since a module has limited bypass diodes.
Even if this algorithm does not need a updating, some algorithm parameters can be modified for the type of PV module used in a DC power optimizer.
In further study, the proposed GMPPT algorithm will be improved and the dependency of system parameters will be completely eliminated. Furthermore, the proposed algorithm will be applied to a flyback converter based microinverter.