**1. Introduction**

In recent decades, the development of power supply systems has exhibited significant growth due to their use in portable systems and equipment, ranging from power supply for the Internet of things (IoT) applications to the energy management of renewable energy sources. In this scenario, the current trend in power electronics systems has required the incorporation of new standards and specifications that must be met, such as higher efficiency, conversion ratios, and power density, amongst others [1]. In these systems, the switching converter is the key of every modern power supply system [2], since it has energy-processing functions aided by suitable control schemes. In this sense, the development of new topologies of switching converters is a topic of interest, as are new structures and/or schemes for the interconnection of converters with high efficiencies. There is also an interest in the application to semiconductor elements with low voltage and/or current stress.

In recent years, a significant number of topologies have been developed that satisfy high transformation ratios, based on isolated and nonisolated schemes, where the implementation is based primarily on the particular application. For example, the main aim in alternating current (AC) power supply systems based on switching converters is to achieve lower total harmonic distortion (THD), a higher power factor, and regulation in the output voltages, as well as higher efficiency [3,4]. In these applications, it is desirable for converters to exhibit galvanic isolation between the output and input of the power system. In the case of direct current (DC) power systems, there are two relevant trends: one

**Citation:** Loera-Palomo, R.; Morales-Saldaña, J.A.; Rivero, M.; Álvarez-Macías, C.; Hernández-Jacobo, C.A. Noncascading Quadratic Buck-Boost Converter for Photovoltaic Applications. *Micromachines* **2021**, *12*, 984. https://doi.org/10.3390/ mi12080984

Academic Editor: Francisco J. Perez-Pinal

Received: 13 July 2021 Accepted: 16 August 2021 Published: 19 August 2021

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is related to the power supply of portable and electronics equipment; the other is related to energy processing and control from renewable sources [5] to develop power systems with high transformation ratios and high efficiency [6,7].

In the emerging renewable energy market, it is a common practice to use switching converters under maximum power point tracking (MPPT) control schemes to obtain the maximum power available in photovoltaic (PV) and/or wind systems. In addition, switching converters must have high conversion ratios, since the voltage levels provided by photovoltaic systems, fuel cells, and/or batteries is a few tens of volts [8,9]. This condition requires systems that allow the processing of energy at the levels of hundreds of volts without or with galvanic isolation capacity.

Currently, switching converters with the capability of increasing or reducing the input voltage for different applications have gained attention. Al–Saffar et al. [4] presented a converter topology based on the interconnection of buck-boost and quadratic buck topologies to obtain high power factor and low output voltage. An approximation for supply systems for light-emitting diode (LED) applications with a high power factor is presented in [10] by Alonso et al. using a quadratic buck-boost converter. The synthesis of a switching converter based on quadratic buck and basic boost topologies was introduced by Nousiainen and Suntio [11,12], where the converter was applied on a photovoltaic system to adapt the energy injected to an inverter. The development of switching converters has led to converters with floating loads [13,14], which restrict their possible applications. In addition, some topologies of circuit synthesis combine the properties of quadratic converters with basic topologies [4,10,11,15,16]. Nowadays, emergent topologies address actual challenges faced by power supply systems for renewable energies, for example, continuous input and output currents, high voltage conversion ratios, common ground path between the input and output ports [14,17–21], and bidirectional power flow properties with quadratic voltage conversion ratios [15,22].

In he technical literature, several solutions exist to obtain switching converters with high voltage conversion ratios. The cascade connection of basic converters is a solution to this problem. Carbajal-Gutiérrez, et al. [23] presented a modeling approach for a quadratic buck converter, where the converter has a high gain to step down the output voltage. In [24], Morales-Saldaña et al. discuss the implementation of a multiloop control scheme in a quadratic boost converter. In [25], Loera-Palomo et al. present a family of quadratic step-down converters based on the noncascade connection of basic switching converters; in [26], a set of converters with a quadratic step-up voltage conversion ratio is introduced. Other quadratic or high-gain converters are presented in [27–30]. In the context of quadratic converters, in recent years, converters with high buck-boost conversion ratios have been appearing [7,16–18,31].

This paper presents a switching converter topology on the basis of the reduced redundant power processing concept, which is based on the interconnection of basic converters in a noncascade structure. The obtained conversion ratio is characterized by a step-up and step-down of the output voltage by a quadratic factor. The proposed converter has a low component count, noninverting output voltage, a common node between the input and output ports, and continuous input current. Additionally, the converter is analyzed with different types of sources and loads where the impact of the PV system in the operation of the converter is investigated .

The remainder of this paper is organized as follows: In Section 2, the proposed converter with wide step-up/down conversion ratio is presented. In addition, a steadystate analysis is given under three scenarios: (1) voltage source–resistive load, (2) PV source–resistive load, and (3) PV source–clamped voltage, to provide insight into the operating conditions of the converter. In Section 3, a representative example is presented to illustrate the main differences in the operating point in steady-state and voltage/current stresses on semiconductor devices. The experimental results of the converter in a PV application are presented in Section 4. Finally, the paper concludes with some remarks in Section 5.
