# Analysis of Subharmonic Oscillation and Slope Compensation for a Differential Boost Inverter
## 1 Introduction
Moreover, differential inverter topologies seem to prevail in price and size due to the utilization of small passive elements of DC-DC converters hence improving the efficiency. In contrast to the conventional H-bridge inverter, the differential boost inverter is a flexible DC-AC inverter topology providing voltage step-up capability and could be a potential candidate for many DC-AC electrical energy conversion applications such as for power processing stage fuel-cell energy system [41; 42], for high quality sine wave generation with a high oscillation frequency [43], for AC-module microinverters in PV systems such as in [44; 45; 46] among others. In stand-alone operation mode, the load is directly supplied by the inverter. Single-phase H-bridge inverters are simple bidirectional converter topologies capable of handling both real and reactive power having their performance evaluated in terms of power quality and stability. Therefore, generating a high quality output voltage with low distortion and good voltage regulation is the main target. Other relevant performance metrics include disturbance rejection, transient response, and insensitivity to load and system parameter variations. These metrics can only be achieved with a design free from any kind of instability. Since its introduction in [47], many studies have dealt with the control design of the differential boost inverter using different approaches and strategies [44; 45; 47; 48; 49]. The focus in most of the works published about this inverter is on the control design. However, the analysis of its nonlinear behavior has not been addressed in the past. Namely, SO has not been studied in this kind of inverter. Therefore the aim of this paper is to apply the Floquet theory for accurately predicting the onset of SO in a differential boost inverter. In contrast to existing works on predicting such a complex behavior in DC-AC inverters based mainly on numerical procedures, here both numerical and analytical approaches are combined to provide a comprehensive study of the systems dynamical behavior. The prediction of this phenomenon is of high importance from both theoretical and practical points of view because it leads to an increase in the ripple of the currents and voltages and this has a harmful effect on the system performances since the overall losses become more significant. The power quality can also be jeopardized if SO is more pronounced since it can increase the THD and the current stress on the switches. Therefore, accurate modeling and stability analysis are necessary for exploring the dynamic behavior and predicting the stability boundaries of DC-AC inverters. The remaining of this paper is organized as follows. In Section 2, the system dealt with in this study is described. In Section 3, the dynamic behavior of the system is explored revealing that the behavior of the system waveforms is phase-dependent. The system is shown to exhibit local instability phenomenon over a specific interval within the main sinusoidal cycle. The onset of the observed bubbling is associated to a SO phenomenon taking place at the fast switching scale. The mathematical modeling is addressed in Section 4 in the continuous-time domain. In order to analyze the observed phenomena in Section 3, Floquet theory is applied to the derived model in Section 5. Thereafter, in Section 6, the stability boundaries in terms of suitable parameters is reported. Finally, in Section 7 the results of the study are summarized.