1. Introduction
Energy is important for the world to provide better living standards and also support every part of other essential elements of society. The problems faced by the conventional energy sources are increases in the cost of fossil fuels, environmental factors, and their effects on human health. Researchers are looking forward to generating pollution-free electricity by means of sustainable energy sources. Sustainable energy sources are naturally available forms such as wind, biomass, solar, fuel cells, and water that have been deemed clean and inexhaustible. Solar energy is predominantly utilized for producing electrical energy among the other sustainable energy sources because of its lower maintenance and minimum operational cost. Development of solar energy harvesting has been gaining more attention recently, and is predominately utilized for stand-alone and grid-connected systems [
1]. Most of the existing solar power generation utilizes the flat solar panel configuration or solar farms. The flat solar PV panel-based energy harvesting systems occupy an enormous quantity of functional space. However, the solar PV tree-based energy harvesting system utilizes only a part of that land space for the equal quantity of energy production. The solar PV tree is an arrangement of solar panels in a tree configuration, which is more advantageous as compared with the flat panel configuration. Solar PV tree-based energy generation is one of the means of electrical energy production in the metropolitan region to save land space and meet the required energy demand of the people. The solar PV tree model is the most viable solution that may be implemented to fulfill the electricity demand exclusively for the power-off period. Additionally, if it produces the excess energy, it may give the power to the grid. A detailed summary of solar tree structure is explained in [
2].
In [
3], the solar PV tree design’s branches have a single PV cell, and it follows the Fibonacci series pattern. In [
4], the semi-dome design was designed to extract the solar energy using the solar PV tree model with tilt angle varying from 0–46°. In [
5], the tree-structured hybrid energy generator utilizing piezoelectric and photovoltaic effects at a nanometer size was demonstrated. In [
6], the two solar PV tree structures based on 3/8 and 2/5 phyllotaxy pattern were discussed, and the results were found to be better as compared with the conventional flat panel arrangement.
The currently available PV module in the market gives a low conversion efficiency of approximately 20%, and its characteristics are affected by its non-linear behavior and the external parameter variation. Owing to the lower conversion efficiency compared with other alternate energy sources, the voltage produced in the PV module is low, and it can be higher with the combination of series PV module. However, it is not possible to operate at the maximum point of the converter under the varying load condition. The generation of power from the PV module changes according to the insolation, module temperature variation, dust, shade, and spectrum from sun. The partial shading condition is one of the most challenging conditions that influence the efficiency of the PV module because of its installation in an open-air environment. To overcome this issue, the MPPT technique is implemented to extract and maintain the maximum power at the output of the solar PV module array, which is the most feasible solution.
Several methods pertaining to MPPT algorithms have been developed to track the optimal point from the PV array under partial shading conditions. Some of the conventional methods are perturb and observe (P&O) [
7], hill climbing (HC), incremental conductance (INC) [
8], neural network (NN) algorithms [
9], soft computing techniques, fuzzy logic controller (FLC) [
10], evaluation-based techniques (differential evolution (DE) [
11], simulated annealing (SA) [
12], particle swarm optimization (PSO) [
13], the genetic algorithm (GA) [
14], cuckoo search (CS) [
15], and artificial bee colony (ABC) [
16]. Among these techniques, the three different algorithms, namely P&O, INC, and NN, are chosen for implementation in the proposed system.
The P&O technique is the classical MPPT algorithm, which is generally used due to its control simplicity. It is very simple and easy to realize and produces better performance in standard test conditions. For the P&O algorithm developed in [
17], the rate of change of PV array output used as input to the proportional–integral controller to produce the different perturb values according to the input change.
The incremental conductance (INC) method with direct control was implemented in [
18]; the selection of suitable iteration step size provides the optimal point quickly. In this technique, the solar PV output is regulated depending upon the maximum power point position, which depends upon the instantaneous and incremental conductance of the PV array.
The soft-computing-based MPPT algorithms such as FLC and NN compute the optimal point with greater accuracy and generates a rapid response when compared to the conventional method. RBFN is one of the NN techniques that has the potential to control the time-varying condition and non-linear effects effectively along with the fastest convergence and easiest network configuration [
19,
20].
The operating voltage for the maximum power point based on solar PV modules is very low. Due to lower voltage, it is not possible to connect the load directly. By using a conventional boost converter, the low voltage is stepped up based on the load requirement. The switching voltage for the boost converter is normally high for the period of conversion time.
In
Figure 1, the general block diagram of the proposed work is illustrated. The current (I) and voltage (V) obtained from the solar PV tree are given to the MPPT algorithms for tracing the optimal point, and they produce the appropriate duty-cycle for the DC–DC boost converter. This paper proposes a unique solar PV tree structure in which the panels are located at the different angle. The conventional boost converter is utilized in this work. The performance of the proposed system is evaluated with the three different conventional MPPT methods of P&O, INC, and the RBFN-NN to obtain the optimum power from the individual module of the solar PV tree. A few attempts have been made in the solar tree concept, but none of them have tried to implement the MPPT techniques so far. Therefore, authors have made an attempt to implement the three different conventional MPPT algorithms with the proposed solar tree structure in this article. The proposed system (solar PV-tree concept) is examined with the constant irradiance and varying irradiance conditions. The three different algorithm values are compared with each other to corroborate that the proposed solar PV tree with RBFN-NN provides the best solution in all the climatic conditions. The different MPPT techniques have been reported in [
21,
22,
23]. The proposed configuration of the solar tree structure with the RBFN MPPT technique provides enhanced output power during the partial shading condition. This MPPT strategy requires less time to reach the maximum peak point, which increases its efficiency and makes it highly robust in the non-linear application.
The organization of this paper is as follows:
Section 2 deals with the structure of the solar PV tree design. In
Section 3, the modeling of the PV system is described with the help of a single diode model.
Section 4 discusses the various techniques of MPPT algorithms, namely P&O, INC, and RBF, to track the optimum power. The design of the DC–DC converter, especially the boost converter, is discussed in
Section 5.
Section 6 presents a complete analytical performance assessment of the different MPPT algorithms under dynamic partial shading conditions. Finally,
Section 7 concludes the proposed work.
3. Mathematical Modeling of Solar PV Cell
The PV cells are manufactured using semiconductor materials with necessary doping in the p–n junction, which are used to allow the current flow once external potential is applied (e.g., temperature and irradiance) [
24]. For obtaining the higher output voltage value, the solar PV cells are interconnected in series configuration. To produce the required larger current, the solar PV modules are interconnected in a parallel manner. In order to estimate the P-V and I-V characteristic curves of the solar PV cells, a single diode model is employed, owing to its simplicity and accuracy.
Figure 4 illustrates the corresponding electrical equivalent model of the single PV cell modeled, which consists of the combination of a diode, a series resistance, shunt resistances, and a current source. The output DC current equation of the equivalent single-diode circuit is represented in Equation (4).
Equation (4) expresses the output current (
I), which consists of the electrical parameters and voltage output (
V) of the solar PV cell,
where
I is current output,
V is voltage output of the solar PV cell,
Ipv is output of photo-generated current and it depends on the temperature related in Equation (5), Is represents the reverse saturation current of the single diode equivalent model,
q is the charge of an electron (1.6021 × 10
−19 °C),
Rsh and
Rse are the shunt and series resistances of solar PV cell, respectively,
k is the Boltzmann constant (1.3806 × 10
−23 J/K),
Ns is the number of cells connected in series,
a is the ideality factor of diode equivalent model, and
T is the absolute operating condition temperature of the solar PV array.
The thermal voltage of the PV cell is described in Equation (6) as follows,
Due to Equation (7), Equation (4) is given by
where
Ipv,n is the nominal solar PV cell current,
Tn is the nominal temperature, Δ
T is the deviation from operating temperature (
T),
KI is the ratio of short circuit current variation to temperature in standard condition,
Gn is nominal irradiance from solar energy, and
G is the irradiance.
where
Isc, and
Voc,n are the short circuit current and open circuit voltage based on nominal operating condition (
Tn = 25 °C and
Gn = 1000 W/m
2), and the ratio of the open circuit voltage to temperature is denoted by
Kv. The typical current versus voltage and power versus voltage characteristics curves of the solar PV panel are depicted in
Figure 5.
5. Boost Converter
The converter is the most essential part of generating the step-up voltage acquired from the solar PV tree according to the load demand. Here, the conventional boost converter is employed to produce a required amount of voltage value. The DC–DC boost converter is illustrated in
Figure 12, which consists of an inductor (
L), capacitor (
C0), diode (
D), and single switch (
S). When the switch (
S) is ON, the direction of the flow of current is from the PV panel (
VPV) to the switch (
S) through the inductor (
L). The inductor (
L) stores energy during this period, and the diode (
D) obtains a reverse biased (
RB) condition. When the switch (
S) is OFF, the diode (
D) becomes forward-biased (
FB), and the stored energy in the inductor (
L) is released. The current takes the path from the solar PV panel (
VPV) to the capacitor (
C0) via the inductor (
L) and diode (
D) during this period. As a result, the load voltage increases according to the PV panel output voltage. The equations [
24] pertaining to the design of the boost converter is given in
Table 1. The parameters are estimated through the expressions.
Figure 13 shows the Bode plot asymptotes for the magnitude and phase of the proposed converter. The Bode plot is plotted based on the state space equation, which is discussed in [
30]. The Bode plot presented in the revised manuscript has the phase margin value of 28, which is the positive value. Therefore, the bode plot information ensures a stable DC–DC feedback control system. The gain margin at the converter switching frequency is analyzed to ensure that the proposed converter has reduced the gain at that point to prevent instability.
6. Result and Discussion
This section deals with the implementation of proposed solar PV tree using MATLAB for the rating of 1278.18 W with the individual solar panel capacity of 213.03 W. The performance of the proposed solar PV-tree is tested with the P&O-, INC-, and RBFN-based MPPT methods for tracking the maximum power in varying environmental condition. The utilized solar PV tree system specification for this work is listed in
Table 2. For the solar PV tree, the six PV panels are connected in a tree structure with a different position, which is discussed in
Section 2. The solar PV tree consists of three layers in which a single solar module presents in the first layer, two solar modules present in the second layer, and three solar modules present in the third layer. The boost converter is used in this work to step-up the solar PV tree voltage. The parameters, such as
Vin = 26.3 V,
Vout = 260 V, duty cycle = 0.9,
L = 1.93 mH, and
Co = 128 µF, are used in the simulation. The switching frequency used in the proposed system is 24 kHz. The orthogonal least squares (OLS) learning algorithm is employed to train the RBFN. The variation of the spread constant is taken as the key deciding factor for RBFN performance. The 3000 data sets have been taken from the PV panel (i.e., voltage and current) under varying irradiation conditions for training the NN. These values are considered the input of the neurons, whereas the duty cycle is considered the output of the neurons. The duty cycle has been decided based on the boost converter gain, voltage, and current values of PV panel. The solar PV-tree along with different MPPT techniques, namely P&O-, INC-, and RBFN-based DC–DC boost converters, are tested separately, and the results are compared for both constant and variable irradiance conditions with constant temperature.
6.1. Constant Irradiance Condition
In this analysis, both the irradiance and temperature are considered as constant for the solar PV tree. The boost converter output and power output of the solar PV tree system using P&O, INC, and RBFN are depicted in
Figure 14a,b. The output power of the proposed solar PV tree system for the constant irradiance condition is tabulated in
Table 3. Simulation results show that the output power generated using P&O-, INC-, and RBFN-based MPPT algorithms is 870.6, 887.8, and 1009 W respectively. From the results, it is clearly shown that the RBFN-based PV system generates better power than the other MPPT methods.
6.2. Variable Irradiance Condition
The proposed system is also validated by varying the irradiance level of the PV system with a constant temperature for calculating the performance evaluation. The different levels of irradiance range between 450–1000 W/m
2 values for six PV panels under 0.5 s variation, which are shown in
Table 4 and
Figure 15. The duty cycle and PWM of the proposed system for the corresponding irradiance are shown in
Figure 16.
Figure 17a,b illustrates the solar PV tree output power and boost converter output power for the different MPPT techniques. The power output of the solar PVtree for different irradiance conditions is listed in
Table 5. From the simulation results, the P&O- and INC-based MPPT produce the output power of 842.8 and 844.8 W, whereas the RBFN-based MPPT method generates 895.4 W output power during the 0–0.5 s period with the lesser oscillation.
The analysis of the proposed method is carried out further for each layer of solar modules in the solar tree structure. The performance of all six PV panels in the solar PV tree using P&O, INC, and RBFN MPPT methods is illustrated in the
Table 6,
Table 7 and
Table 8. The proposed solar PV tree using P&O-based MPPT to track the maximum power under varying irradiance conditions is depicted in
Figure 18, and the performance results are given in
Table 6. The output power produced by one of the solar modules is 197.4 W when the irradiance level is 1000 W/m
2 and 77.3 W under 450 W/m
2 irradiance conditions. The simulation result clearly reveals that the P&O-based MPPT method produces more oscillation during the changes in irradiance condition, whereas the constant value is for the standard irradiance condition.
The same type of analysis is also performed for the INC-based MPPT technique, and the results are shown in
Figure 19 and
Table 7. This method gives the output power of 197.9 and 91.5 W for 1000 and 450 W/m
2 irradiance condition, respectively. By comparing the obtained results from P&O and INC method, it is visibly seen that the INC-based MPPT technique tracks the optimum power with lesser oscillation nature than the P&O technique.
The simulation results are obtained with a similar type of analysis for the RBFN-based MPPT technique, which are given in
Figure 20. and
Table 8. In this method, the maximum power of 209.2 W is generated during the standard irradiance condition and 191.79 W is generated at 450 W/m
2 irradiance condition. From the simulation results of all the three methods, it is concluded that the RBFN-MPPT technique with DC–DC boost converter gives the best tracking rather than the other two algorithms.
6.3. Hardware Implementation
The real time implementation of the solar tree is shown to validate the performance of the proposed MPPT strategy, as shown in
Figure 21. The solar tree consists of a 16 PV array connected in an Eight Series–Eight Parallel configuration. The total power generated from the PV is 1.2 kW. A dSPACE real time controller is used in this work to generate the gate pulses to the converter switch with a signal frequency of 24 kHz. A boost type dc/dc converter is used to amplify the input voltage to the desired level.
Two different modes of partial shading conditions are considered to verify the proposed MPPT method experimentally in varying weather conditions. The results of these conditions are as illustrated in
Figure 22,
Figure 23 and
Figure 24.
Figure 22 shows the experimental results of the system with the P&O-based MPPT technique. The entire tracking process in the P&O-based MPPT technique takes more time to reach the maximum power point (MPP). The power obtained from the boost converter by implementing the P&O-based control strategy are 284 W for 600 W/m
2 and 722 W for 900 W/m
2.
The experimental results of the INC-based MPPT technique are shown in
Figure 23. The power output of the boost converter obtained by using the INC-based MPPT strategy is 432 W for 600 W/m
2 and 828 W for 900 W/m
2. The INC method performs better than the P&O-based control technique in terms of extracting maximum power. Nevertheless, the INC method lacks minimization of the convergence speed to track the maximum power and oscillates around the MPP for a longer time.
To overcome the above said two limitations, an RBFN-based control technique is proposed in this work. The experimental results of the RBFN-based control strategy are shown in
Figure 24. The RBFN-based MPPT technique is faster in terms of tracking the MPP, thus eliminating the oscillation during partial shading condition. The power output obtained using the proposed MPPT technique is 540 W for 600 W/m
2 and 942 W for 900 W/m
2. The RBFN-based MPPT technique is the most suitable MPPT strategy for varying weather conditions.