Introduction

1Over the last few decades, the solar energy field has attracted much attention from researchers [1,2,3,4]. As known in the literature, the PV module characteristics are highly dependent on environmental conditions such as solar irradiation, temperature, and wind, etc [5,6,7,8]. Solar irradiation can occur uniformly or non-uniformly on a PV array. The P-V characteristic of a PV array exhibits one peak under uniform irradiation conditions, and this peak is called the maximum power point (MPP). Tracking this MPP is always a critical issue in a PV system to maximize the power transfer from the PV array to the load. Over the past decades, many maximum power point tracking (MPPT) methods have been introduced to address this issue [9, 10]. Among these methods, we found conventional methods such as perturb and observe (P&O) Hill Climbing (HC), and incremental conductance (INC). However, the main drawback of these methods is that they have strong oscillations around the MPP in steady state, resulting in power losses of the available energy. To solve this problem, many researchers have tried to improve these conventional methods to reduce the steady-state oscillations. These improved methods are based on variable step size of duty cycle controllers [11, 12]. In addition, in [13], the authors presented a new sliding mode control for optimizing the power output of a stand-alone PV system. Although the implementation of conventional methods can be easily [14 15 16], they were unable to obtain the true MPP under PSC. Because, under the non-uniform solar irradiation caused by partial shading, the P-V characteristic of a PV array has several peaks. One of them is the global peak (GP)  that represents the GMPP, and the others are the local peaks. In addition, due to the inability to track the real MPP under PSC, the power output of the PV array can be reduced by 10–70% [17,18,19,20,21].

To address this problem, many GMPPT algorithms have been introduced in these references [22,23,24,25,26,27,28] to solve the complexness of the nonlinear behavior of PV characteristics and providing optimal solutions under partial or full shading conditions. Where we find most of them belong to soft computing (SC), evolutionary computation (EC), and swarm intelligence (SI) algorithms. Among the SC methods, we find the artificial neural networks (ANN). in [29] authors presented an application of an ANN for optimization of the out power of a PV alimented the dc motor. In addition, In [30] a detailed survey on ANN-based PV MPPT techniques was presented. From this survey, it turns the accurate results are good using ANN. But, when used a large number of hidden nodes this technique needs a longer computational time. Hence, it needs a complex hardware implementation.

In addition to that, several algorithms of intelligence artificial are introduced [31, 32] in order to extract the maximum power of PV array with high efficiency under partial or full shading. But, these techniques might present a poor convergence rate and slow convergence time [33]. On the other hand, the SI methods have a good convergence rate and fast convergence compared to EC techniques [34, 35]. Although these SI methods are better than the genetic algorithm (GA) and differential evolution (DE) methods. But, they have limitations. For example, the response time always linked to the initial placement of the particle. Which makes them inflexible and more complex [36]. However, the implementation of these methods is more complex [26]. To overcome these complexity found in the EC and SI methods, the scanning algorithm is introduced in [37] where all the MPP’s values are stored in a microcontroller. Yet, this method is simple and easy to implement in low-cost microcontrollers. But, under storing all the possible MPPs, this method takes a long processing time. Because the scan is started from the point of the short-circuit current (ICC) to the open-circuit voltage (VOC) of the P-V characteristic. Hence, this techniques interrupt the system operation when scanning the entire control range between the VOC and ICC, which yields power losses.

The aim of this work is to present an improved scanning method in order to track the GP under dynamic PSCs. The objective of this method is to reduce and limit the scan interval, which avoids the passage through the short-circuit point of the P-V characteristics. In addition, it eliminates the open-circuit of the PV string during the scan interval in order to prevent disconnection of the PV system. All these modifications allow this proposed method to track the GMPP with good response time and high efficiency under dynamic PSCs. Moreover, the simple structure used in this proposed method will ensure reduced complexity of implementation, which reduces the cost of the PV system.

The rest of this paper is organized as follows: Section II presents the proposed methodology. The results and discussion are depicted in Section III. Finally, Section IV summarizes this work.

Methodology

Description of the Entire PV System

Figure 1 presents the entire PV system developed in this study, which consist of  a PV string, a Boost converter, a GMPPT controller based on the scanning algorithm, and a load. The PV panel used in this work is based on the one-diode model of PV cells [6, 11]. In addition, the PV cell equivalent physical circuit is depicted in Fig. 2.

$$ {I}_c={I}_{phc}-{I}_0\left(\mathit{\exp}\frac{q\left({V}_c+{R}_{sc}\ {I}_c\right)}{aKT}-1\right)-\frac{\left({V}_c+{R}_{sc}\ {I}_c\right)}{R_{shc}} $$
(1)

The output current of the PV cell is presented by Eq. (1) [6], where Vc is the input voltage of the PV cell, Io is reverse cell saturation current, Iphc is the input current of PV cell, K is the value of the Boltzmann’s constant (k = 1.3807*10–23 JK-1). q is the value of the electronic charge (q = 1.60221019 C), And ɑ is the quality factor of the diode.

Fig. 1
figure 1

Schematic of the entire PV system with the scanning controller

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Fig. 2
figure 2

PV cell equivalent physical circuit

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The reverse cell saturation current I0 represents by Eq. (2)

$$ {I}_o={I}_{oc}{\left(\frac{T}{T_r}\right)}^3\exp \left(\frac{qE_{GO}}{GK}\left(\frac{1}{T_r}-\frac{1}{T}\right)\right) $$
(2)

The input current of PV cell Iphc represents by Eq. (3)

$$ {I}_{phc}=\left[{I}_{sc}+{K}_1\left(T-298,18\right)\right]\frac{G}{1000} $$
(3)

Table 1 presents the values of the irradiation taken for all simulation tests. Under PSC1, the shading scenarios was performed with the irradiation value of three PV panels set to 1000 W/m2 and one PV panel set to 500 W/m2. Thereafter, the shading of the other test is taking by varying the number of the shaded panels of the PV string. Otherwise, the temperature value of module PVs was fixed to 25°C in all test simulations of PSCs.

Table 1 The value of the irradiation taken for all simulation tests
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Figure 3 presents the P-V characteristics under the various conditions of irradiation. During PSC, the P-V characteristic of a PV string mainly exhibits two peaks resulting from the presence of two irradiance levels, one is the GP and represents the GMPP of the PV string and the other is the local peak. In addition, the first peak is delivered at Vmpp1 (voltage corresponding to this peak) and the other at Vmpp2. It is assumed that the scan of the P-V characteristic under PSC3 is included a max search interval of search points. For that, the analysis of the classical and the improved scanning methods is based on the P-V characteristic under PSC3.

Fig. 3
figure 3

The P-V curves characteristics of a PV String under diverse irradiation

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Analyse of Classical and Improved Scanning Method for PV System under PSC

Classical Scanning Method

The principle of the scanning GMPPT technique is based on the scan of the curve P-V characteristic in order to find the global power of the PV system using simple instructions. When the duty cycle is varied, the value of V, I, P, and D are stored in own vectors at each iteration. Next, it controls the converter by the corresponding value of the global duty cycle in order to maintain the out power of the PV system at the maximal value under various PSCs. Figure 4 presents the scan interval points on the P-V curve using the classical scanning method. It is observed that the scanning of the P-V characteristic starts from the point of the short-circuit current (ICC) which corresponds to 0 V and stops at 0.95 × Voc.

Fig. 4
figure 4

The scan points on the P-V curves Under PSC3 using the classical scanning method

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Figure 5 depicts the proposed method's sequence, which consists of three steps. The first step is the scanning loop which contains the data backup of the vectors D(i), P(i), V(i), I(i), obtained in each iteration when the duty cycle is varied. Next, the second step consists of the determination of the GP using Eq. (4) [37]. It is noted that GP of the P-V Characteristics is the maximum value between all the values of P (i) recorded. And the last step is the boucle of detection change PSC.

$$ \mathrm{GMPP}=\operatorname{Max}\left(\mathrm{P}\left(\mathrm{i}\right)\right) $$
(4)
Fig. 5
figure 5

Flowchart of the proposed scanning method

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Figure 6 presents the output power of the PV string under PSC3 by using the classical scanning method. From this first test, it is observed that the scanning method finds the GMPP with good efficiency and a response time is almost equal to 1.95 s. But, the drawback of this method is the short circuit of the PV string during the scan interval when each PSC change. This, of course, affects the efficiency of the PV array in long term.

Fig. 6
figure 6

The output power of the PV string under PSC3 by using the classical scanning method

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Improved Scanning Method

Figure 7 presents the search interval of the scan points on the P-V curves under PSC3 using the classical and improved scanning method. It is observed that the improved scanning method being less scan interval compared to the classical method. The idea of this method is to estimate the scan interval by limiting the search interval of duty ratio. This limitation is giving by some analysis based on PV characteristics as mentioned in Fig. 3. The first step does not start the scan with a short-circuit. In addition, the value of Vmpp2 (voltage corresponding to the second peak) does not exceed the value 0.85 × Voc. Therefore, we force the improved scanning method to stop at the value of 0.85 × Voc. So, we will win time to extract the GMPP due to limiting the search interval of the P-V curve.

Fig. 7
figure 7

The scan points on the P-V curves Under PSC3 using the classical and Improved scanning method

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Figure 8 illustrates the result of the simulation under PSC3. it is observed that the output power of the PV string is equal to the value of the GP. The irradiation value of each PV model is presented in Table 1. It can be observed that a scan of the P-V curve by the improved scanning method does not start with a short-circuit and stops at the value of 0.85 × Voc. So, This modification improved the response time (1,4 s) compared to the classical scanning method (1,95 s).

Fig. 8
figure 8

The output power of the PV string under PSC3 by using the improved scanning method

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Results and Discussion

The global schematic of the PV system designed in the proteus environment is presented in Fig. 9. The PV string used is composed of six PV panels having the same characteristics. Next, the value of the load is designed by considering the value of the load optimal of the PV string. The DC-DC boost converter is used in order to implement the improved scanning GMPPT. The control of this converter is done through the TC4420 driver. The role of this driver is to boost the value of the duty cycle between a threshold to attack the transistor. The simulation results of the proposed method are  displayed in the graphic analysis as shown in Fig. 9.

Fig. 9
figure 9

The global schematic of the PV system designed in the proteus environment

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The simulation results of the improved scanning method are shown in Fig. 10 under various PSCs. The PV string is subjected to different PSCs (PSC1, PSC2, PSC3, and STC). The irradiation value of the PV module for each PCS is taken in Table 1. As mentioned in Fig. 10, the tracking speed with the improved method is faster than that of the classical scanning algorithm. To clarify more, the proposed method only takes 1.4 s. Thus, the tracking speed of the improved method is 1.39 times faster than that of the classical scanning method. Also, we can be observed the same conclusion under all PSCs with a fast response time than that of the classical scanning. Furthermore, a comparison between the classical and Improved scanning algorithms is done in Table 2. The first test case under PSC1 presents a good efficiency (98.89%) and speed response time (1.4 s). In other’s cases, it is obtained the same response time (1.4 s) compared with the first test. With a maximum efficiency up to 99.50%. from this comparison, can be deduced in all test cases that the efficiency and the response time of the PV system are improved by 0.4% and 0.55 s respectively compared to the Scanning method [37].

Fig. 10
figure 10

The output power of the PV string Under Varoius PSCs

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Table 2 Comparisons of classical and modified scanning methods under various PSCs
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Although the proposed method is simple and easy to implement in low-cost microcontrollers. But, under a change of the insolation value during the scanning operation, this proposed method is unable to track a real GMMP as shown in the results obtained in Fig. 11. On the other hand, when the PSCs change again on the outside of the scanning loop, this method is able to restart the scan in order to track the corresponding GMPP of the PV string. So, it can be used in commercial MPPT controllers in order to increase the energy production of the PV string under PSC while decreasing the cost of the system.

Fig. 11
figure 11

The results simulation of the output power of the PV string under a change of the insolation value during the scanning loop

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Conclusions

In this paper, a simple GMPPT controller based on an improved scanning method is proposed. The idea of this improvement is initiated by analyzing the scan interval points on the P-V curve using a conventional scan method. Then, with the analysis based on PV characteristics, we could estimate the scan interval by limiting the search interval of the duty cycle, and thus improve the tracking speed. The obtained results showed that the proposed method efficiently tracks the GMPPT under different CSPs and has a good response time (1.4 s), which improves the response time of the PV system by 0.55 s compared to the conventional scanning method [37]. Thus, the simple structure used in this proposed method will significantly reduce the implementation complexity, which will lead to a reduction in the cost of the PV system. Although the proposed method is simple and easy to implement in low-cost microcontrollers, it has a limitation in terms of tracking the actual GMPP when a change in the insolation value, during the scan operation, occurs.

Based on the results presented in this paper, the next step of our research will focus on solving the problem of the proposed method’s inability to track the actual GMPP during a change in the insolation value.