Comparative Study of Buck-Boost, SEPIC, Cuk and Zeta DC-DC Converters Using Different MPPT Methods for Photovoltaic Applications

Abstract

The power produced in a photovoltaic (PV) system is highly dependent on meteorological conditions and the features of the connected load. Therefore, maximum power point tracking (MPPT) methods are crucial to optimize the power delivered. An MPPT method needs a DC-DC converter for its implementation. The proper selection of both the MPPT technique and the power converter for a given scenario is one of the main challenges since they directly influence the overall efficiency of the PV system. This paper presents an exhaustive study of the performance of four step-down/step-up DC-DC converter topologies: Buck-Boost, SEPIC, Zeta and Cuk, using three of the most commonly implemented MPPT techniques: incremental conductance (IncCond), perturb and observe (P&O) and fuzzy logic controller (FLC). Unlike other works available in the literature, this study compares and discusses the performance of each MPPT/converter combination in terms of settling time and tracking efficiency of MPPT algorithms, and the conversion efficiency of power converters. Furthermore, this work jointly considers the effects of incident radiation variations, the temperature of the PV panel and the connected load. The main contribution of this work, other than selecting the best combination of converter and MPPT strategy applied to typical PV systems with DC-DC power converters, is to formulate a methodology of analysis to support the design of efficient PV systems. The results obtained from simulations performed in Simulink/MATLAB show that the FLC/Cuk set consistently achieved the highest levels of efficiency, and the FLC/Zeta combination presents the best transient behavior. The findings can be used as a valuable reference for the decision to implement a particular MPPT/converter configuration among those included in this study.

1. Introduction

Over the last few decades, photovoltaic (PV) energy has become one of the most relevant sources of renewable energy. PV systems are top ranked among renewable energy supplies [1]. By the year 2021, the capacity of PV solar power installed in the world had reached approximately 942 GW, including both on-grid and off-grid capacity, according to [2]. Nevertheless, PV panels convert only a small amount of the incident solar irradiation (15–20%), producing electricity with a very low conversion efficiency [3], which reduces the cost-benefit ratio of PV systems. Moreover, the power generation of a PV system depends on environmental conditions such as solar radiation and temperature, along with the characteristics of the connected load [4]. The power of a PV module is maximum at the inflection point of the P-V characteristic, known as the maximum power point (MPP). To maximize the conversion efficiency of a PV panel despite variations in environmental and load conditions, the use of a maximum power point tracking (MPPT) method is indispensable [5].

Over the years, a variety of MPPT techniques have been developed, such as Hill Climbing (HC), Particle Swarm Optimization (PSO), Fractional Open Circuit Voltage (FOCV), Incremental Conductance (IncCond), Fractional Short Circuit Current (FSCC), Perturb and Observe (P&O), Sliding Mode Control (SMC), Artificial Neural Network (ANN), Genetic Algorithm (GA), Cuckoo Search (CS), fuzzy logic controller (FLC) and Firefly Algorithm (FA), among others [6,7,8,9,10,11,12,13]. All of those techniques vary in several respects, such as implementation complexity, effectiveness, tracking speed, tracking accuracy, cost, and hardware requirements [14]. Among all of them, P&O, IncCond and FLC techniques, have been widely used in practical applications [15,16,17]. P&O and IncCond, which are regarded as conventional MPPT methods, have the advantages of being suitable for any PV generator. They work quite well under most conditions and they are simple to implement on a low-cost digital controller [18]. However, both algorithms oscillate around the MPP and fail to converge under sudden meteorological changes [19,20]. On the other hand, FLC is a robust artificial intelligence (AI) method which can reach high MPP tracking efficiency and accuracy [21]. This technique was conceived relying on human understanding of process control and is based on qualitative rules [22]. The FLC method does not require any mathematical model. Furthermore, its implementation is simpler when compared to other AI techniques [23]. Nevertheless, the absence of a systematic method for formulating the membership functions is the main drawback of an FLC method. They mainly are based on the designers’ experience and knowledge about the system. In PV systems, the use of an MPPT method requires for its implementation a DC-DC converter, which can be seen as an impedance adapter between the PV panel and the connected load. The DC-DC power converter is controlled through its electronic switch by a signal generated by the MPPT technique called the duty cycle [24]. There are many DC-DC converters utilized for renewable energy applications and which can be classified into two categories, namely, isolated and non-isolated converters [1]. Although both categories have their own advantages and disadvantages, non-isolated DC-DC topologies are still a more advantageous and feasible option to integrate with renewable energy systems [25].

Buck-Boost, Buck, Boost, SEPIC, Zeta and Cuk are the most frequently used non-isolated converters for PV applications [26]. Among these converters, the topologies Boost and Buck present simplicity, high efficiency and low-order circuits [27]. However, they lack output voltage flexibility, which may limit their use. Indeed, the Boost converter can only increase voltage and the Buck converter can only reduce voltage [28]. Therefore, in PV system battery charging, for instance, both Boost and Buck converters are unfit to charge the battery continuously with MPPT operation. If the battery voltage is lower than maximum power voltage of the PV panel, MPP tracking is not possible in Boost converter; on the other hand, if the battery voltage is greater than the maximum power voltage of the PV panel, MPP tracking is not possible in a Buck converter [29]. Since Buck-Boost, SEPIC, Zeta and Cuk topologies are capable of generating a higher or lower output voltage than the PV generator, they can achieve MPP tracking regardless of changes in weather conditions and connected load. Hence, those topologies are preferable for the MPPT principle [25,30].

Over the years, many comparative studies in the field of PV systems and concerned with power converters and MPPT techniques have been conducted. The majority of these works have focused on analyzing the tracking efficiency of the MPPT algorithms and their impact on the power generation of the PV panel, as shown in [4,7,14,18,21,24,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55]. On the other hand, not much attention has been given to the behavior of the DC-DC power converter, though the choice of the suitable DC-DC converter is essential because it has a relevant role in the overall efficiency of the PV system and its reliability. It should be noted that the behavior of the power converter varies depending on the parameters and its operating conditions, such as switching frequency, duty cycle, voltage and current levels, load impedance, continuous conduction mode (CCM) and discontinuous conduction mode (DCM), among others. Thus, it is a task for researchers to define which MPPT/converter set, from the conversion efficiency point of view, performs better in a given scenario. To the best of the authors’ knowledge, there are few recent works taking this approach, as seen in [27], where the authors compare the conversion efficiency of two DC-DC converters (Boost and Buck) working with three different MPPT techniques (IncCond, P&O and Temp). This work shows that the P&O/Boost combination performed with the highest power conversion efficiency. In [56], the conversion efficiency of seven DC-DC converters (Buck-Boost, Boost, Buck, Zeta, SEPIC, Luo and Cuk) is compared, but only operating with the P&O algorithm. In this paper, the authors conclude that the Buck-Boost converter performed better than the rest. In [57], the conversion efficiency of four DC-DC converters (Zeta, ZVS Zeta, SEPIC and ZVS SEPIC) working with two MPPT techniques (IncCond and P&O) is compared. This paper shows that the IncCond/ZVS Zeta configuration achieved the best performance.

Taking into account the abovementioned analysis, this work presents a new comparative study between four non-isolated DC-DC converters (Buck-Boost, SEPIC, Zeta and Cuk) operating with three of the most popular MPPT algorithms (IncCond, P&O and FLC). The study compares and discusses the performance of each MPPT/converter set in terms of their settling time and average steady-state efficiency. Unlike comparative studies available in the literature, this work considers the effects of variations in incident radiation, PV panel temperature and connected load on the performance of the MPPT methods and on the conversion efficiency of each power converter. Thus, this paper provides valuable information for choosing the most suitable MPPT/converter configuration, from the efficiency point of view, for certain weather and load conditions.

The study has been conducted based on simulations implemented with MATLAB/Simulink. In order to obtain more accurate and comparable results, all converters have been designed to present the same inductor ripple current and capacitor ripple voltage levels for a given operating condition. In addition, the passive components of each converter have been simulated in the presence of non-idealities according to commercial values. Furthermore, a precise model for the Kyocera KC85TS commercial PV module has been used.

The paper is structured as follows: Section 2 briefly describes a typical PV system with MPPT controller. In Section 3, a concise description of the main characteristics of the DC-DC converters as well as the sizing of their components is given. Section 4 provides the principles of operation of the MPPT techniques. Simulated results and comparative analysis are provided in Section 5. Section 6 summarizes the conclusions of the paper.

2. PV System Description

In a PV system, when the PV generator is connected directly to the load, its operation point is determined by the generation and load curves’ intersection, which commonly does not coincide with the MPP of the PV module. Moreover, on the one hand, radiation and temperature variations impacts generation curve changes, while on the other hand, the type of load connected to the PV module affects the load curve. Under these conditions, the PV system is unable to operate at the MPP most of the time, with an ensuing loss of available solar energy. To surmount this issue, a DC-DC converter is placed between the load and the PV module, as is shown in Figure 1. Thus, an MPPT algorithm regulates the converter’s duty cycle in order to match the apparent impedance of the PV panel to the impedance at the MPP.

3. DC-DC Converters

Buck-Boost, SEPIC, Zeta and Cuk are non-isolated DC-DC power converters which are able to generate an output voltage larger or smaller than the input voltage magnitude, so they are also called step-down/step-up converters. In comparison to step-down and step-up topologies, step-down/step-up converters are able to cover the entire I–V characteristics of a PV panel. This fact helps MPPT operation to be conducted perfectly in a PV system, regardless of variations in atmospheric and load conditions.

3.1. Buck-Boost Converter

The Buck-Boost converter is simple and inexpensive to implement because it only contains a capacitor and a coil as energy storage elements [28]. It should be noticed that its input current is always discontinuous since the switch is in series with the generator, which implies that the current has many harmonic components, high input ripple and significant noise problems [58]. To handle this problem, large capacitors or LC filters are required. Moreover, in a conventional Buck-Boost converter, the output voltage has opposite polarity than the input voltage, which represents its main issue [59]. Figure 2a shows the structure of a conventional Buck-Boost converter.

3.2. Cuk Converter

Unlike the Buck-Boost converter, where energy transfer is associated with the inductor, energy transfer for the Cuk converter depends on the capacitor C₁ as shown in Figure 2c. The inductor L₁ on the input filters the DC supply current, preventing large harmonic content [60]. Its continuous input current reduces the size of the input filter capacitor by reducing the current stress on it. In addition, this topology also guarantees the continuity of the output current [61]. Another advantage of this converter is that the control terminal of the electronic switch is grounded, which simplifies the gate drive design. On the other hand, like the Buck-Boost converter, the Cuk converter generates an inverted output voltage [62].

3.3. Single-Ended Primary Inductance Converter (SEPIC)

Just like Cuk converter, the SEPIC converter has an inductor at the input. Hence, the input current waveform is continuous with a low ripple level [63], which is suitable to achieve high-precise MPPT performance. Another benefit of this configuration is the isolation between the output and the input by the capacitor C₁, as shown in Figure 2b. The capacitor C₁ protects against a short circuit or an overload of the output [64]. Moreover, the classical SEPIC topology has the advantage (when compared to Buck-Boost and Cuk topologies) that both output and input voltages have the same polarity [65]. In addition, the SEPIC converter, like the Cuk converter, has the advantageous feature of the switch control terminal connected to ground [58]. On the other hand, the SEPIC converter has a discontinuous output current, which implies that a large output capacitor filter is necessary to smooth the current.

3.4. Zeta Converter

The Zeta converter, similar to the SEPIC converter, does not suffer from the polarity reversal problem [66]. Furthermore, the Zeta topology not only has low output voltage ripple, which facilitates the output regulation task, but also its uniform output current allows the use of smaller capacitors, which improves the load performance [25,67]. Those features make the Zeta converter a better candidate when voltage quality and output power is critical [68]. On the other hand, the Zeta converter, like the Buck-Boost converter, suffers from the drawback of having a discontinuous input current [69], which can affect the MPPT performance. Another important issue that must be considered in this converter is that the control terminal is not grounded. Thus, a complex high side switch driver circuit is required [26]. Figure 2d shows the structure of the Zeta converter.

3.5. Design of the DC-DC Converters

The passive components of each converter were calculated by using the equations in

Table 1. Setting equations.

Parameter	Buck-Boost	Cuk	SEPIC	Zeta
$\frac{V_o}{V_s}$	$-\frac{D}{1-D}$	$-\frac{D}{1-D}$	$\frac{D}{1-D}$	$\frac{D}{1-D}$
$L_1$	$\frac{V_s·D}{\Delta I_{L1}·f}$	$\frac{V_s·D}{\Delta I_{L1}·f}$	$\frac{V_s·D}{\Delta I_{L1}·f}$	$\frac{V_s·D}{\Delta I_{L1}·f}$
$L_2$	-	$\frac{V_s·D}{\Delta I_{L2}·f}$	$\frac{V_s·D}{\Delta I_{L2}·f}$	$\frac{V_s·D}{\Delta I_{L2}·f}$
$C_1$	$\frac{V_o·D}{\Delta V_{C1}·f·R}$	$\frac{V_o·D}{\Delta V_{C1}·f·R}$	$\frac{V_o·D}{\Delta V_{C1}·f·R}$	$\frac{V_o·D}{\Delta V_{C1}·f·R}$
$C_2$	-	$\frac{V_o\left(1-D\right)}{8·\Delta V_{C2}·L_2·f^2}$	$\frac{V_o·D}{\Delta V_{C2}·f·R}$	$\frac{V_s·D}{8·\Delta V_{C2}·L_2·f^2}$

. All converters were sized to present the same inductor ripple current (ΔI_L) and capacitor ripple voltage (ΔV_C) levels for certain operating conditions. The operation conditions were set as follows: ΔI_L1 = 10%, ΔI_L2 = 20%, ΔV_C1 = 5%, ΔV_C2 = 2%, DC power supply voltage V_s = 17.4 V, output voltage magnitude V_o = 12 V, load resistor R = 2 Ω and PWM switching frequency f = 30 kHz. In order to incorporate the effect of the losses in the passive components, the calculated values were replaced by the most similar commercial values, so as to include the DC resistance (DCR) of the inductors and the equivalent series resistance (ESR) of the capacitors. It should be noted that the losses in the semiconductors were partially estimated, since only the value of static drain-to-source on-resistance (R_DS(on)), in the case of the mosfet, and both forward slope resistance (R_on) and forward voltage drop (V_F), in the case of the diode, were considered.

Table 2. Passive components of the DC-DC converters.

	Buck-Boost		Cuk		SEPIC		Zeta
Parameter	Calculated Value	Commercial Value	Calculated Value	Commercial Value	Calculated Value	Commercial Value	Calculated Value	Commercial Value
$L_1$	233.5 µH	220 µH DCR = 75 mΩ Coilcraft PCV-2-224-05L	572.1 µH	560 µH DCR = 90 mΩ Coilcraft PCV-2-564-08L	572.1 µH	560 µH DCR = 90 mΩ Coilcraft PCV-2-564-08L	572.1 µH	560 µH DCR = 90 mΩ Coilcraft PCV-2-564-08L
$L_2$	-	-	197.3 µH	180 µH DCR = 48 mΩ Coilcraft PCV-2-184-10L	197.3 µH	180 µH DCR = 48 mΩ Coilcraft PCV-2-184-10L	197.3 µH	180 µH DCR = 48 mΩ Coilcraft PCV-2-184-10L
$C_1$	340.1 µF	330 µF ESR = 22 mΩ Panasonic EEUFR1H331L	136.1 µF	150 µF ESR = 42 mΩ Panasonic EEUFR1H151	136.1 µF	150 µF ESR = 42 mΩ Panasonic EEUFR1H151	136.1 µF	150 µF ESR = 42 mΩ Panasonic EEUFR1H151
$C_2$	-	-	20.8 µF	22 µF ESR = 340 mΩ Panasonic EEUFR1H220	340.1 µF	330 µF ESR = 22 mΩ Panasonic EEUFR1H331L	20.8 µF	22 µF ESR = 340 mΩ Panasonic EEUFR1H220

shows the summary of the passive components of each converter.

Table 3. Semiconductor devices.

Component	Description
Mosfet	IRF540Z Static Drain-to-Source On-Resistance ${\mathrm{R}}_{\mathrm{DS}\left(\mathrm{on}\right)}=26.5 \mathrm{m}\Omega$
Diode	MBR20100CT Forward Voltage Drop ${\mathrm{V}}_{\mathrm{F}}=0.8 \mathrm{V}$ Forward Slope Resistance ${ \mathrm{R}}_{\mathrm{on}}=15.8 \mathrm{m}\Omega$

shows the values of the commercial semiconductors used.

4. Maximum Power Point Tracking Algorithms

4.1. Perturb and Observe (P&O) Method

This technique is extensively applied in commercial devices and is the basis of most of the more sophisticated algorithms presented in the literature [48]. The P&O method is widely utilized because of its low cost and simplicity of implementation [70]. This technique consists of disturbing the PV panel voltage in a certain direction through a disturbance of the duty cycle of the DC-DC converter (Δd), and then observing the behavior of its output power. If the power increases, the disturbance continues in the same direction; otherwise, the system is perturbed in the opposite direction. The process is repeated periodically, so in steady state the power oscillates around the MPP, thus wasting some of the energy available in the PV panel. To guarantee proper behavior both dynamic and in steady state, a suitable size for Δd must be carefully selected [71]. The main drawback of this method is the occasional shift of MPP due to rapid changes in climatic conditions, such as in the case of moving clouds [72]. Figure 3 shows the flowchart of this technique.

4.2. Incremental Conductance (IncCond) Method

The IncCond technique is widely utilized because of its high steady-state tracking accuracy and good adaptability for rapid changes in weather conditions [6,73]. This algorithm is based on the principle that the slope of the P-V characteristic of the PV module is zero at the MPP $\left(\frac{dP}{dV}=0\right)$, negative on the right and positive on the left [21]. Thus:

$$\frac{dP}{dV}=I+V\frac{dI}{dV}\cong I+V\frac{\Delta I}{\Delta V}$$

(1)

Then (1) can be written as:

$$\frac{\mathsf{\Delta }I}{\mathsf{\Delta }V}=-\frac{I}{V} (\mathrm{at} \mathrm{the} \mathrm{MPP})$$

(2)

$$\frac{\mathsf{\Delta }I}{\mathsf{\Delta }V}>-\frac{I}{V} (\mathrm{left} \mathrm{of} \mathrm{the} \mathrm{MPP})$$

(3)

$$\frac{\mathsf{\Delta }I}{\mathsf{\Delta }V}<-\frac{I}{V} (\mathrm{right} \mathrm{of} \mathrm{the} \mathrm{MPP})$$

(4)

The MPP is traced by comparing the instantaneous conductance $\left(\frac{I}{V}\right)$ with the incremental conductance $\left(\frac{\Delta I}{\Delta V}\right)$. When the MPP is reached, the converter’s duty cycle must remain unchanged because the PV panel voltage (V_PV) coincides with the maximum power voltage of the PV module (V_MPP). In this case, ΔV is zero and the incremental conductance calculation must be omitted, and only the PV panel current must be evaluated. In the event that the MPP changes, a perturbation in the duty cycle must be performed to seek the new MPP. The main disadvantage of this algorithm (compared to P&O) is the increase in hardware and software complexity, due to the mathematical operations required. This latter causes an increase in computation times, which limits the sampling rate for the measurement of voltage and current signals [70]. Figure 4 shows the flowchart of this algorithm.

4.3. Fuzzy Logic Controller (FLC) MPPT Method

FLC is a type of AI strategy that uses heuristic logic for solving complex problems. Because of its simplicity and effectiveness, this approach has become very popular for the control of both linear and non-linear systems. Over the years, this method has demonstrated its outstanding features for the design of high-performance MPPT controllers with the advantage of not requiring any mathematical model of the PV system [74,75]. However, this control approach does not provide a systematic method; instead, it bases its design according to the trial and error method and information that comes from an expert’s knowledge of the system, which represents its main drawback [16,76]. Takagi–Sugeno and Mandami are two of the most frequently used fuzzy inference systems for developing an FLC [77].

Figure 5 shows the block diagram of a typical FLC. In the fuzzification phase, the input signals are transformed into linguistic variables. In the inference phase, the control actions are executed by means of the knowledge base, which is described in terms of If-Then rules and their membership functions. In the defuzzification phase, the fuzzy information is converted back to numerical information using some defuzzification method, such as center of gravity (CoG), or Mean of Maxima (MoM), among other [78,79,80].

For the FLC used in this work, the fuzzy inputs were determined as the slope (S) and the power variation (ΔP_PV) defined from the Power-Voltage curve of a PV panel. S and ΔP_PV are described by Equations (5) and (6), respectively. For the output variable, the duty cycle increment (ΔD) was determined, which allows calculation of the duty cycle value to control the DC-DC power converter. The duty cycle value is defined by Equation (7). Figure 6 shows the membership functions for the output and inputs of the FLC. For both output and inputs, asymmetrical triangular membership functions were adopted, and their values adjusted by trial and error employing the MATLAB Fuzzy Logic Toolbox.

Table 4. Rules for the FLC.

S	NB	NS	ZO	PS	PB
ΔPPV
NB	PB	PS	ZO	NS	NB
NS	PB	PS	ZO	NS	NB
ZO	PS	PS	ZO	NS	NS
PS	PB	PS	ZO	NS	NB
PB	PB	PS	ZO	NS	NB

shows the fuzzy rule base used. Details of the FLC design can be found in [23].

$$S\left(n\right)=\frac{\Delta P_{PV}\left(n\right)}{\Delta V_{PV}\left(n\right)}=\frac{I_{PV}\left(n\right)·V_{PV}\left(n\right)-I_{PV}\left(n-1\right)·V_{PV}\left(n-1\right)}{V_{PV}\left(n\right)-V_{PV}\left(n-1\right)}$$

(5)

$$\Delta P_{PV}\left(n\right)=P_{PV}\left(n\right)-P_{PV}\left(n-1\right)$$

(6)

$$D\left(n\right)=D\left(n-1\right)+\Delta D\left(n\right)$$

(7)

where n is the sampling time, P_PV(n) is the PV module power, V_PV(n) is the PV module voltage, I_PV(n) is the PV module current and D(n) is the duty cycle of the power converter.

5. Simulations

This section presents the results of the simulations carried out. The general scheme of the PV system shown in Figure 1 was implemented. The PV array was made of one Kyocera KC85TS module.

Table 5. Electrical characteristics of the Kyocera KC85TS commercial PV panel [81].

Parameters	Values
Maximum power current (IMPP)	5.02 A
Maximum power voltage (VMPP)	17.4 V
Maximum power (PMPP)	87 W ± 10%
Short circuit current (ISC)	5.34 A
Open circuit voltage (VOC)	21.7 V
Temperature coefficient of ISC	2.12 × 10−3 A/°C
Temperature coefficient of VOC	−8.21 × 10−2 V/°C
Max system voltage	600 V

presents its main electrical specifications. Details of its modeling can be found in [4]. Figure 7 shows the power-voltage curves obtained for the PV panel at different levels of radiation and temperature. The values of the passive components and semiconductors used in each converter are those shown in Table 2 and Table 3, respectively. The PWM switching frequency was set at 30 kHz. It should be noted that the switch drivers were not considered, they were simulated as ideal components. Moreover, a capacitor was connected between the PV panel and the DC-DC converters to suppress input voltage ripple and filter ripple current. A value corresponding to the commercial Panasonic EEUFR1H102 capacitor (C = 1000 µF, ESR = 16 mΩ) was used.

Figure 8 shows the simulation scheme developed for testing the SEPIC converter operating with the FLC controller. A similar structure was implemented for the other converters and MPPT methods studied in this work. To test the steady-state follow-up efficiency, different tests were performed. First, sudden changes in the radiation profile were applied, keeping a constant temperature of 25 °C. The radiation was varied between 250 W/m² and 1000 W/m², as shown in Figure 9a. Next, abrupt variations in the temperature profile were applied, keeping a constant radiation of 1000 W/m². The temperature was varied between 15 °C and 30 °C, as shown in Figure 9b. Both tests were performed considering four different load resistance values (R = 2 Ω, R = 5 Ω, R = 10 Ω and R = 20 Ω). Each MPPT/converter configuration was compared in terms of efficiency in power produced by the PV panel and the conversion efficiency of the converters, according to the expressions (8) and (9), respectively. Figure 10 shows the waveforms of PV panel current (I_PV), duty cycle, PV panel voltage (V_PV), PV panel power (P_PV) and converter output power (P_out) for the Buck-Boost converter acting under radiation variations; Figure 11, Figure 12 and Figure 13 show the same waveforms for the Cuk, SEPIC and Zeta converters, respectively.

$${\mathsf{\eta }}_{\mathrm{MPPT}}=\frac{{{\displaystyle \sum }}_{i=1}^n{\mathrm{P}}_{\mathrm{PV}}}{{{\displaystyle \sum }}_{i=1}^n{\mathrm{P}}_{\mathrm{MPP}}}\times 100$$

(8)

where P_PV is the power produced by the PV panel, and P_MPP is the ideal maximum power generated by the PV panel.

$${\mathsf{\eta }}_{\mathrm{converter}}=\frac{{{\displaystyle \sum }}_{i=1}^n{\mathrm{P}}_{\mathrm{out}}}{{{\displaystyle \sum }}_{i=1}^n{\mathrm{P}}_{\mathrm{PV}}}\times 100$$

(9)

where P_out is the output power provided by the converters.

5.1. MPPT Tracking Efficiency under Radiation Variations

Figure 14 shows the summary of the results obtained for the tracking efficiency of the MPPT algorithms for variations in incident radiation. It can be observed that the best performance was achieved by the FLC algorithm operating with the Cuk converter and a connected load of 5 Ω, reaching 99.94% efficiency (Figure 14b), while the worst performance was presented by the P&O algorithm working with the Zeta converter and 2 Ω load, reaching an efficiency of 98.76% (Figure 14a). Figure 15 shows the average efficiency achieved by each MPPT algorithm considering all load conditions. It can be observed that, regardless of the converter used and the value of the connected load, the highest percentages of efficiency were achieved by the FLC algorithm, with the FLC/Cuk configuration being the one that achieved the best performance with an average efficiency of 99.87%. On the other hand, the worst performance was presented by the P&O/SEPIC configuration, reaching an average efficiency of 99.18%.

5.2. Converter Efficiency under Radiation Variations

Figure 16 shows the summary of the results obtained for the conversion efficiency of the converters for variations in incident radiation. One can observe the influence of the value of the connected load on the performance of the converters. It is clear that the conversion efficiency of the converters tends to be reduced as the value of the load resistance reduces. On the other hand, it can be seen that the best performance was achieved by the Cuk converter when operating with the FLC algorithm and a connected load of 20 Ω, reaching an efficiency of 91.67% (Figure 16d). The lowest performance was presented by the Buck-Boost converter when working with the P&O algorithm and a load of 2 Ω, reaching an efficiency of 80.09% (Figure 16a). Figure 17 shows the average efficiency achieved by each converter considering all load conditions. It can be observed that regardless of the algorithm used and the value of the connected load, the highest percentages of efficiency were achieved by the Cuk converter. The FLC/Cuk configuration was the one that achieved the best performance with an average conversion efficiency of 89.43%. On the other hand, the worst performance was presented by the P&O/Buck-Boost configuration, reaching an average efficiency of 87.26%.

Figure 18, Figure 19, Figure 20 and Figure 21 show the behavior of the Buck-Boost, Cuk, SEPIC and Zeta topologies, respectively, for temperature variations.

5.3. MPPT Tracking Efficiency under Temperature Variations

Figure 22 shows the summary of the results obtained for the tracking efficiency of MPPT algorithms operating at different temperatures. It can be seen that the best performance was achieved by the FLC algorithm, reaching an efficiency of 99.94% operating with either the Cuk converter or the SEPIC converter, and with a connected load of 2 Ω in both cases (Figure 22a). The worst performance was presented by the P&O algorithm operating with the SEPIC converter and a load of 20 Ω, reaching an efficiency of 98.57% (Figure 22d). Figure 23 shows the average efficiency achieved by each MPPT algorithm considering all load conditions. It can be seen that, regardless of the converter used and the value of the connected load, the highest percentages of efficiency were achieved by the FLC algorithm, with the FLC/Cuk configuration being the one that achieved the best performance with an average efficiency of 99.77%. On the other hand, the lowest average efficiency was presented by the P&O/SEPIC configuration, reaching a value of 98.98%.

5.4. Converter Efficiency under Temperature Variations

Figure 24 shows the summary of the results obtained for the conversion efficiency of the converters for variations in the temperature of the PV panel. As can be seen, the value of the connected load has a direct effect on the performance of converters, with converters achieving lower efficiency when operating at higher load current levels (lower load resistance). On the other hand, the best performance was achieved by the Cuk converter when operating with the FLC algorithm and a connected load of 20 Ω, reaching an efficiency of 91.63% (Figure 24d). The lowest performance was presented by the Buck-Boost converter when working with the P&O algorithm and a load of 2 Ω, reaching an efficiency of 79.67% (Figure 24a). Figure 25 shows the average efficiency achieved by each converter considering all load conditions. It can be observed that, regardless of the algorithm used and the value of the connected load, the highest percentages of efficiency were achieved by the Cuk converter, with the FLC/Cuk configuration being the one that achieved the best performance with an average conversion efficiency of 89.51%. On the contrary, the worst performance was presented by the P&O/Buck-Boost configuration, reaching an average efficiency of 86.89%.

5.5. Transient Tracking Time

The following test was performed in order to analyze the transient behavior: the PV system was simulated considering an incident radiation of 1000 W/m² and PV panel temperature of 25 °C. For each MPPT/converter configuration, the convergence time (τ) was determined as the instant in which the power reached 95% of the ideal maximum power in the PV module, as recommended in [37]. Figure 26, Figure 27, Figure 28 and Figure 29 show the responses of the MPPT techniques acting with the Buck-Boost, Cuk, SEPIC and Zeta converters, respectively. The test was carried out for each of the load resistance values used above (R = 2 Ω, R = 5 Ω, R = 10 Ω and R = 20 Ω). Figure 30 shows the summary of the results obtained, from which it is observed that the MPPT algorithms respond faster to lower load resistance values. The FLC/Zeta combination with a connected load of 2 Ω presented the fastest transient response with τ = 57.78 ms (Figure 30a), whereas the P&O/SEPIC configuration with a connected load of 20 Ω presented the slowest response with τ = 303.20 ms (Figure 30d). Figure 31 shows the average transient tracking time obtained for each MPPT/converter configuration, where it can be observed that the FLC/Zeta combination was the one that reached the fastest average response with τ = 70.91 ms, whereas the P&O/SEPIC configuration was the one that presented the slowest average response with τ = 288.38 ms.

6. Conclusions

This work enables the selection of the best combination of converter and MPPT strategy applied to typical PV systems with standard DC-DC power converters and the most commonly used MPPT techniques. An exhaustive analysis of the performance of four topologies of non-isolated step-down/step-up DC-DC converters (Buck-Boost, SEPIC, Zeta and Cuk), operating with three different MPPT methods (P&O, IncCond and FLC), used to maximize the electrical power produced in PV generation systems, has been presented. The study was developed based on simulations in Simulink/MATLAB. The transient response and average steady-state efficiency of each MPPT/converter combination were analyzed and compared, considering variations in incident radiation, PV panel temperature and connected load.

The results obtained showed that the value of the connected load has a significant impact on the overall efficiency of the photovoltaic system. It was possible to verify that, in general, when a lower load value is used, the efficiency of the converters and the response times of the MPPT algorithms decrease. On the other hand, regardless of the converter used, all MPPT techniques present excellent performance, with all of them reaching average efficiencies above 98%. Although the three techniques produce similar efficiencies, FLC was slightly superior among them all, followed by IncCond and then P&O. Additionally, it appears that regardless of the MPPT algorithm used, the Cuk converter presented the highest conversion efficiency among all converters; consequently, the FLC/Cuk combination had the best performance of all. On the contrary, the Buck-Boost converter showed the lowest conversion efficiencies, with the P&O/Buck-Boost configuration being the worst. Regarding convergence time, the FLC/Zeta configuration showed the lowest average response time to reach MPP and the P&O/SEPIC configuration had the slowest response.

Finally, this research can be used as a valuable reference for making decisions about whether to implement a particular MPPT/converter configuration among those included in this study.