## 1 Introduction  
Photovoltaic (PV) installations are a growing market due to the objective of reducing greenhouse emissions by 2030 by, at least, 55% [1]. In addition, PV installations can be used to replace backup diesel generations, reducing urban pollution in large cities. Additional benefits of PV systems are the availability of solar energy at the production site, avoiding the need of fuel transportation required by traditional diesel generators; better usability of large surfaces such as rooftops; and simple scalability of the PV power generation. In addition to the modularity, PV installations also require mitigation of the detrimental effect of the partial shading conditions on series-connected PV panels (named strings), in which small shades could significantly reduce the power production [2]. One suitable solution to mitigate this problem is to introduce voltage equalizers [2, 3], which provide a path for the current difference between two (or more) series-connected modules. This solution avoids the activation of the bypass diode associated to the shaded module; otherwise, such a module will operate in short-circuit condition without producing power. Those voltage equalizers can be designed with classical inductor switched topologies or using switched capacitor solutions [2], which reduce the converter size and electromagnetic pollution [4; 5; 6; 7] but introduce discontinuous input or output currents. However, since the voltage equalizers are designed to interact with series-connected modules, introducing (or subtracting) modules from the PV installation requires a disconnection of the whole string. Finally, voltage equalizers do not introduce a voltage boosting factor; hence, several PV modules must be connected in series to reach the input voltage needed by classical grid-connected inverters. Another strategy to mitigate the effect of partial shading conditions, and to provide modularity to the PV installation, concerns the use of microinverters [8]. Those devices enable to easily increase (or decrease) the PV installation depending on changes in the load demand without major changes in the installed devices. Moreover, the microinverter avoids the series connection of PV modules; hence, no bypass diodes are activated, which reduces the impact of partial shading conditions. The classical two-stage microinverter is a small power system formed by a PV module, a first stage to perform the tracking of the maximum power point (MPPT) and the regulation of the PV voltage, and a second stage in charge of the grid synchronization and the regulation of the DC-link between both stages; such a microinverter structure is observed in Figure 1.  
The first stage of the microinverter includes a DC/DC converter to match the PV voltage with the DC-link voltage, as reported in [8; 9], where that DC/DC converter must be regulated to track the maximum power point (MPP) of the PV source in a particular environmental condition. Such a control system is formed by two components [9]: an MPPT algorithm, which defines the optimal PV voltage reference \(v_{r}\), and a high-bandwidth controller, to ensure that the PV voltage \(v_{pv}\) follows the MPPT reference. The MPPT algorithm usually requires the measurement of the PV voltage and current, \(v_{pv}\) and \(i_{pv}\), while the controller could require the measurement of additional internal variables of the DC/DC converter such as the inductor current \(i_{L}\) or DC-link voltage \(v_{b}\). Finally, the controller generates the control signal \(u\) of the DC/DC converter. The grid connection is performed using an inverter, which has two main objectives: interact with the grid to deliver the PV power, and regulate the DC-link voltage. This last objective is very important in PV systems, since the grid interaction forces a single-phase inverter to inject sinusoidal power at double the grid frequency, which produces a sinusoidal voltage oscillation at double the grid frequency in the DC-link.