## 1 Introduction
Several power converters reported in literature, such as two- and three-level inverters, H5, H6, and HERIC, have found commercial and academic research acceptance [14, 15, 16]. Traditional inverters are unable to provide high efficiency at higher power ratings; therefore, converter topologies are moving toward multilevel structures. Among the various multilevel inverters, cascaded H-bridge multilevel inverters (CHB-MLI) have several advantages as compared to other converters [17, 18, 19, 20, 21]. The use of CHB inverters also opens up the prospect for removal of transformers from PV systems. MLIs are more attractive because of their lower device stress and low _dv/dt_. A CHB made up of \(n\) full bridges (\(4n\) power switches) can synthesize \(2n+1\) voltage levels when the supply voltage is the same for each full bridge. Reduction in switches per output voltage levels can be achieved in CHB structures easily, if different supply voltages are selected for each full H-bridge [20]. Due to the higher number of DC voltage sources used in CHB-MLIs, their application is restricted for higher voltage levels. In due course, asymmetrical CHBs will evolve, until DC voltage sources can be replaced by capacitors. The topology used in this paper consists of two asymmetrical H-bridges and is known as hybrid MLI (HMLI) for generating nine output voltage levels. The DC voltage source (in place of a PV panel) supplies one of the full H-bridges, whereas a capacitor supplies the other one. By appropriately controlling the ratio between the two voltages, different output levels can be generated. This facilitates the elimination of bulky transformers, which makes the overall system lighter and more efficient. However, the removal of the transformer gives rise to leakage current. Due to the change in CMV, leakage current flows though the PV panel, which depreciates the lifespans of the PV modules. Leakage current can be mitigated using several methods, such as by changing converter topology, including filters [22], changing modulation schemes [23, 24], and altering control schemes [25, 26]. Few methods are employed for changing converter topology (e.g., the conventional H-bridge is modified by adding more switches to form the familiar H5 and H6 converters). The leakage current can be reduced by including an extra filter, as reported in [PERSON], [PERSON] et al. [22]. The switched CMV can be kept constant by using a precise modulation scheme. Modification in the modulation schemes of conventional converters is one of the solutions for reducing leakage current. Multicarrier pulse width modulation (MC-PWM) and space vector modulation (SVM) are two well-known modulation techniques used in MLIs [24, 25]. The SVM technique is more productive due to better switching control. However, it requires regress efforts for implementation. In [PERSON], [PERSON] et al. [24], SVM is used to reduce the leakage current in transformerless PV inverter topology. However, switching state selection is not easy in terms of practical implementation. MC-PWM also increases the computational burden because of a higher number of carrier signals. Among the reported control schemes, model predictive control (MPC) is one of the better control schemes because of its robust dynamic and static characteristics. In this work, an optimized finite control set (FCS) MPC is utilized for overall control and for reducing leakage current from PV panels [27, 28, 29, 30, 31, 32]. This paper uses a transformerless HMLI PV system that synthesizes different multilevel output voltage levels. Capacitor voltage balancing and the elimination of leakage current is achieved through a modified FCS-MPC scheme. The number of computational burdens is minimized to attain optimum results by adjusting the selection of switching vectors. The control algorithm is also optimized for compilation in any microcontroller. Normalization and weighted techniques are also implemented to obtain improved results [32]. The proposed control structure and converter architecture are discussed in Section 2.