A fast and accurate global maximum power point tracking controller for photovoltaic systems under complex partial shadings

The operating conditions of partially shaded photovoltaic (PV) generators created a need to develop highly efficient global maximum power point tracking (GMPPT) methods to increase the PV system performance. This paper proposes a simple, efficient, and fast GMPPT based on fuzzy logic control to reach the point of global maximum power. The approach measures the PV generator current in the areas where it is almost constant to estimate the local maximums powers and extracts the highest among them. The performance of this method is evaluated firstly by simulation versus four well-known recent methods, namely the hybrid particle swarm optimization, modified cuckoo search, scrutinization fast algorithm, and shade-tolerant maximum power point tracking (MPPT) based on current-mode control. Then, experimental verification is conducted to verify the simulation findings. The results confirm that the proposed method exhibits high performance for complex partial irradiances and can be implemented in low-cost calculators.


INTRODUCTION
The power of a photovoltaic generator and its efficiency are strongly linked to the load variation and the climatic conditions [1]- [3]. Various researches have been carried out on this topic to improve the efficiency of this type of renewable source independently of the variation of the irradiance and temperature on one side and load variation on the other side. These researches gave birth to maximum power point tracking (MPPT) methods that track the maximum power point, which have yielded satisfactory results if the generator is exposed to uniform irradiance. Among them, the well-known hill-climbing (HC) [4], incremental conductance (IC), and perturb and observe (P&O), or newer with an adaptive search step like [5], and in [6], the MPPT efficiency is improved by the combination between the algorithm based on fuzzy logic and the IC method, or optimized fuzzy logic control with metaheuristic optimization technique [7] to improve the MPPT efficiency for grid-connected photovoltaic units under uniform irradiances. However, the expansion of solar The presented work is subdivided into six sections. In section 2, the PV generator characteristics under the two conditions, uniform irradiance and PSC are shown. Section 3 details the proposed algorithm. Section 4 explains the design and procedure research. Section 5 is devoted to the simulation and experimental results. In the last section, a conclusion is drawn.

ELECTRICAL CHARACTERISTICS OF PV GENERATOR 2.1. PV generator under uniform irradiance conditions
The area occupied by a PV generator increases with the number of PV modules connected in series and parallel, increasing the likelihood of its exposure to non-uniform irradiance due to shadow. This phenomenon, called the PSC, changes the behavior of the PV generator. Figure 1 shows three identical modules connected in series with three bypass diodes. The Dp1, Dp2, and Dp3, are connected in parallel with PV1, PV2, and PV3, respectively. These diodes protect the panels from being damaged due to their operation in the hotspot region. In the uniform irradiance, the three modules are exposed to the same irradiance G1=G2=G3; where G1, G2, and G3 are the solar irradiance of PV1, PV2, and PV3 panels, respectively. In this case, the global power of three panels keeps the same form as the case of a single module with a single MPP. However, its voltage increases, thus increasing its maximum power too.  (1) and (2) [9], [10]: where Isc_str is the PV string short-circuit current, and Voc_str is the PV string open-circuit voltage.

PV generator under partial shade conditions
In this case, PV1, PV2, and PV3 are exposed to different irradiance levels, G1, G2, and G3, respectively, where G1>G2>G3. This condition leads to a current curve with three stairs, as shown in Figure 3(a), and a power curve with three local maximum power points (LMPP), as shown in Figure 3 (G1), only the PV1 panel generates the power, while the other two panels, PV2 and PV3,  are short-circuited by diodes Dp2 and Dp3, respectively. In the second stair, where the LMPP2 occurs  between the voltages Voc1 and Voc2, the two panels, PV1, and PV2, operate with the same current while the  PV3 remains short-circuited by the diode Dp3. For the last zone, where the LMPP3 is located between Voc2 and Voc3, the three panels PV1, PV2, and PV3 operate with the same current. The current and power shapes are illustrated in Figures 3(a) and (b) respectively. The LMPP2 point in Figure 3(b) is the largest among the other LMPPs, so this point is the GMPP delivered by the PV generator. The open-circuit voltage of each panel varies slightly with the irradiance variation, so the panels PV1, PV2, and PV3 can be assumed to have the same open-circuit voltage (Voc). Consequently, the voltages Voc1, Voc2, and Voc3 shown in Figure 3(a) and (b) can be approximated by Voc1≈Voc, Voc2≈2Voc, and Voc3≈3Voc. Therefore, the voltages at LMPPs can also be approximated to Vm1≈0.8Voc, Vm2≈(1+0.8)Voc, and Vm3≈(2+0.8)Voc [9]. By similarity, in the general case where there are (Ns) identical series-connected PV modules exposed to partial irradiances, the PV generator current pattern has (Ns) stairs corresponding to the (Ns) area. Let us define a zone as the range of voltages between the two voltage Voc (J-1)=(J-1)Voc and the voltage VocJ=JVoc, Voc is the panel open-circuit voltage, J (J=1,2,…, Ns) is the zone number. The shape of the power curve will have an LMPP on each zone, and the LMPP current and voltage in a zone numbered J is given by (3) and (4) [9], [10]: where ImJ and VmJ are respectively the current and the voltage of the LMPP in zone J, and IscJ the short-circuit current in zone J.

PROPOSED GMPPT METHOD
The proposed method provides simplicity in hardware implementation and increases the speed and precision of reaching the GMPP of the shaded PV system, whatever the complexity of shading conditions. This method is based on the following concepts: i) the subdivision of the PV generator voltage curve into zones, whose number is equal to the panels number in series. Each zone contains a single LMPP; the zone of order n is between the two voltages (n-1)Voc and nVoc, where Voc is the open-circuit voltage of each panel; ii) the current measurement in each zone is performed in the region that is almost constant and close to the short-circuit current Isc; iii) the estimation of the maximum power value at each LMPP point in each zone is based on a technique called the 0.8Voc method; and iv) the jump on the zones, which indeed contain an LMPP lower than GMPP (without taking a new current measurement point in these zones). The proposed method flowchart, presented in Figure 4, is divided into several steps.

Initialization
First, the algorithm is started with an initialization step, which gives the initial values of the indices (J=0, N=1, M=0), that determine the measurement, test zones (the zone (J) is the current area of GMPP. The zone (J+N) is the area to compare with the zone (J), M is the jumping index). The PV generator parameters are: the number of panels connected in series (Ns), and the open-circuit voltage Voc of a single generator panel. Vref_J is the voltage that will be given to the DC/DC converter regulator to set the PV generator voltage to this voltage, IJ is the current of the PV generator measured in zone J at the reference voltage Vref_J; initially, the algorithm starts with the zone (0), which corresponds to Vref_J=0=0 and IJ=0=0.

Calculation of the PV generator reference voltage to be given to the DC/DC converter regulator
To set the voltage of the PV generator in a zone (J+N) at the desired value, a DC/DC converter regulator connected with the PV generator is used to force the PV voltage to follow its reference Vref_J+N given by (5): The reference Vref_J+N corresponds to the middle of the zone (J+N), which is between the two voltages (J+N-1)Voc and (J+N)Voc, as indicated in Figure 5. At this point, the PV current is almost constant and equals the short-circuit current of the chosen zone, IPV≈Isc_J+N.

Isc current measurement
The PV current, corresponding to the reference voltage Vref_J+N in the zone (J+N), must be measured in the right part of the zone, where it is almost constant equal to Isc_J+N. To do this, two measured points, a and b, are considered, at which the voltages are Vref_J+N(a)=Vref_J+N and Vref_J+N(b)=Vref_J+N +Va_b, where Va_b is the voltage difference between the two points a and b as indicated in Figure 6. To verify that IPV ≈ Isc_J+N, two conditions should be satisfied. The first one is: with PPV_a=IPV_aVPV_a and PPV_b=IPV_bVPV_b. The second one is: where EI is the accepted current deviation, if one of the two conditions is not fulfilled, a shift of two points a and b by one step (∆step) back is performed until reaching the level of Isc_J +N. The choice of EI is so that the two measurements of the currents IPV_a and IPV_b are taken in the stair between the two currents Isc and Im of this zone. Therefore, the maximum current deviation of this stair is between the current Isc and Im, and according to (1), Isc-Im (1-0.9) Isc=0.1 Isc by consequence EI <0.1.

Comparison between the two estimated powers
The comparison is made between the powers generated in two zones; zone J is assumed to be the current GMPP zone, and zone (J+N) is the new zone to be tested. The two maximum estimated powers of the two zones (J) and (J+N) are given by: where PPVmaxJ and PPVmaxJ+N are the maximum estimated powers in zone J and zone J+N, respectively. A comparison between the two powers can be established using the following relation: If the power PPVmaxJ is less than PPVmaxJ+N, the latter replaces PPVmaxJ by replacing J by J+N and IscJ by IscJ+N.
Otherwise, the power PPVmaxJ is greater than PPVmaxJ+N, and the algorithm will go to the jump step.

The jump to the following zones
In the case where the power PPVmaxJ +N is less than PPVmaxJ, and since the current IscJ+N is greater than the currents of the zones, which follow it, the algorithm compares PPVmaxJ with the power PPVmaxJ+N+M of the zones, which follows the zone J+N using the current IscJ+N without making a new measurement of the current according to the relation: where M is the offset or jumps index; it increments to 1 each time PPVmaxJ> PPVmaxJ+N+M. If condition (13) is not satisfied, the algorithm makes a jump without measuring the current on the J+N+M zones.
The algorithm repeats the previous steps (without initialization) until the last zone Ns, determined by the number of panels connected in series. After scanning all the zones, zone J, which is between the two voltages (J-1)Voc and the voltage JVoc, is the zone that contains the GMPP.

Fuzzy logic control based MPPT
This step is to reach the LMPP point of zone J corresponding to the GMPP point. In the literature, there are several methods of following LMPP, and among them, the MPPT is based on fuzzy logic control commonly known as MPPT-FLC [32]. This method does not rely on the mathematical model of the system. This approach uses a variable search step to quickly reach the maximum point and lower the ripple around this point [3], [32]. That increases the PV generator efficiency and robustness in facing load variations and weather conditions.

RESEARCH METHOD 4.1. MATLAB simulation
The block diagram of the system under study is shown in Figure 7. The simulation model is performed using the MATLAB/Simulink SimPowerSystems toolbox environment. The system is composed of a PV string with five series-connected solar panels of type Samsung 250 Watt. Their parameters are shown in Table 1. This string is connected with a DC/DC converter feeding a variable resistance. It is controlled by two proportional integral (PI) controllers in a cascade [33], as shown in Figure 8. The boost converter and PI controller parameters are gathered in Table 1. The control of the PV string is indirectly [2] ensured by the proposed GMPP algorithm, which provides the value of the PV reference voltage (VPV_ref) for the regulator of the DC-DC converter. The latter provides the appropriate duty cycle value to manage the PWM boost converter and set the PV generator voltage (VPV) at its reference value (VPV_ref).
Several irradiance profiles are proposed according to the values of irradiances for the five panels to evaluate the proposed algorithm performance, as shown in Table 2. Figure 9 show the four P-V patterns 1-4 used for the simulation test. This choice is adopted to give different locations for the GMPP. For the first case, all the panels are exposed to the same irradiance level without shading, and in the second case, the GMPP is on the left side of the PV curve. In the third case, the GMPP is in the middle, and in the fourth case, the pattern contains two MHP.
The proposed algorithm is compared with SFA [13] and ST [30], which are considered among the fastest methods based on the exploitation of the P-V pattern. It is also compared with two metaheuristic methods: HPSO [24] and MCS [23]. The three aspects of comparison are: i) the ability to reach the true where Pmax is true GMPP, T0=0s is the initial time, and Tf =1s is the final time.

Hardware setup
The experimental verification of the proposed MPPT is ensured using an emulator; it is a controlled DC power supply driven by photovoltaic power profile emulation (PPPE). It emulates the behavior of the PV generator, which is five identical modules connected in series with the same characteristics as those used in the simulation, as shown in Table 1. Three shapes of the shadings are considered, as shown in Figure 10(a)-10(c). These shapes are ensured by PPPE interface software.
The converter used is a buck-boost converter with L=1 mH, C1=1000 uF, and C2=470 uF. The algorithm is implemented on a low-cost and mid-range card (ARDUINO DUE) [34]. Figure 11 represents the overall assembly. The proposed algorithm, which is developed using Simulink, is implemented on an Arduino Due board through the library provided by MATLAB. Its effectiveness was compared with the MCS method chosen among the methods used previously in the simulation, thanks to its simplicity in the face of the limitations of the target card capacities.  Table 3 gives the performances of these methods for the four forms of irradiance. All the simulated methods have reached the true GMPP for the different forms of irradiances, and this is thanks to the process of these methods, which scan the whole range of the PV voltage or make jumps on the zones where there is no GMPP.  The HPSO method had the longest response time due to the number of particles chosen (in this case, there are three particles) and the random choice of the initial positions of these particles. Nevertheless, it keeps high efficiency in all patterns. For example, for pattern 1, the response time of HPSO is 0.25 s with a transition efficiency of 98.23%. On the other hand, the SFA method gives an efficiency of less than 96.23% with a response time of 0.18 s, and this is because the movement of particles in the HPSO is directed towards the GMPP point, which will give a power convergence in the transient state until reaching the GMPP. However, the search is done at predefined intervals in the non-heuristic method (SFA, ST, or proposed one).
The MCS gives high transition efficiency and shorter response time than the HPSO method in the four patterns. The SFA method uses the notion of MPT [28] to limit the search interval between the two voltages Vmin and Vmax with Vmax=0.9Voc_str, Voc_str is the PV string open-circuit voltage, Vmin=PGMPP/Impp_STC, where PGMPP is the most considerable PV power over the scanned interval and Impp_STC is the PV generator current in MPP under STC conditions. Then the Vmin is the voltage of the point on the power line PMPT=Impp_STC VPV, which has the power PGMPP as shown in Figure 16. Therefore, Vmin changes at each new point of PGMPP whose power is greater than the previous one, and the highest Vmin value corresponds to the maximum power point in the interval [Vmin Vmax].
As shown in Table 3, the transition efficiency decreased with decreasing GMPP power of the PV generator due to the widening search interval between Vmin and Vmax, as shown in Figure 16. For example, for pattern 2 with PGMPP=706W, its minimum search interval is between Vmax=168 V and Vmin=80 V, which results in an efficiency of 98.14%. On the other hand, in Pattern 3 with PGMPP=406 V, its minimum search interval is between Vmax=168 V and Vmin=46 V, which gives an efficiency of 95% less than that provided in pattern 2.
The SI method makes jumps on the zones where the current almost remains fixed to the left of the maximum point LMPP (LHS-MPP) by the mean of the current regulator, which makes the reference current equal to the Isc of this zone with the relation Iref =Isc=Impp/0.8 where Impp is the LMPP point current reached. While each time, it is necessary to look for the LMPP point in the right zone (RHS-MPP) of this point before making a current jump on the zone (LHS-MPP), as shown in Figure 17. Consequently, the number of (RHS-MPP) zones and their voltage widths will decrease the efficiency of this method and increase its response time. This conclusion is confirmed by the simulation results shown in Table 3. For the four patterns, the initial point is V0=0.8Voc-str, therefore V0=1870.8=150 V, and the widths (L) of the RHS-MPP zones from pattern 1 to pattern 4 indicated by Figures 12-15, are: L1=2 V, L2=30 V, L3=40 V and L4=43 V; respectively. In contrast to the other previous methods, the proposed method remains very efficient with a very short response time compared to the others for all patterns as long as the number of panels in a series remains fixed (five panels). This feature is owing to its research process, which needs only two measuring points in the middle of each zone n (n: 1… Ns) between two voltages nVoc and (n+1)Voc to estimate the maximum power of this zone and to determine at the end the global maximum power between them.  Figure 18 shows the tracking performance for three patterns with the results obtained for pattern 1 in Figure 18(a), pattern 2 in Figure 18(b), and pattern 3 in Figure 18(c). The interpretation of the results obtained is: a. Pattern 01: The MCS method missed the GMPP point for this shape because of its process, which is based only on the difference in voltage between its three particles [23]. The proposed method finds the GMPP with a voltage of VGMPP=26 V after a search time that equals t=14.2 s. This is the half of time needed by the MCS method (t=30.2 s), and this is thanks to the procedure of the proposed method, which scans the voltages V1=28 V, V2=62 V and makes a jump on the zones which remain according to the relation (13). (a) (b) (c) Figure 18. The results obtained, (a) pattern 1, (b) pattern 2, and (c) pattern 3

CONCLUSION
In this paper, a simple FLC based approach for global maximum point power GMPP tracking under partial shading conditions is proposed. This approach is based on estimating the maximum power using the principle of the 0.8 Voc method and the current measured in the area where it almost remains constant and equal to the short-circuit current of the shaded PV modules. The proposed method is compared to four recent GMPPT methods; two are heuristic, and the two are based on the PV curve. The comparison was made by examining the ability to achieve the real GMPP, convergence time, and efficiency. The obtained results revealed that the proposed method gives a significant improvement and a higher performance than the other methods regardless of the form and complexity of the partial shading. However, some gaps need to be filled in future work that has not been considered, such as adding a system to differentiate between the shape of the partial shading and the rapid change in irradiance, as well as the type of converter used with its corrector to improve performance further when monitoring the reference voltage.