# Trajectory Control Approach for Single-Stage Soft-Switching Grid-Tied Inverters
## 1 Introduction  
With the increasing adoption of local and distributed energy sources, as well as energy storage devices, there is growing interest in developing miniaturized and lightweight modular Power Conditioning Systems (PCS). Photovoltaic (PV) energy and energy storage systems (ESS) are among the most important and widely used applications. When these direct current (DC)-based systems connect to alternating current (AC)-based legacy grids, critical interoperability issues arise, necessitating advanced control capabilities [1, 2]. In addition to achieving high power density, grid-tied inverters should offer advanced controls, such as volt-VAR compensation, voltage ride-through, anti-islanding protection, etc. To achieve such complex control, this paper employs a finite state machine (FSM) model on digital signal processing platforms for single-stage soft-switching grid-tied inverters. Grid-tied inverters are typically categorized into three types depending on the PV module arrangement: centralized inverters, string inverters, and module-integrated inverters, commonly known as microinverters [3, 4, 5, 6, 7, 8]. Microinverters for single PV modules with power capacities ranging from 300 to 400 W have become increasingly popular in grid-connected PV systems. This increased adoption is largely due to their elimination of bulky low-frequency transformers, maximum power point tracking (MPPT), low installation costs, and user-friendly 'plug-and-play' configuration, which is enhanced by their modular and flexible structure with communication capabilities. Over the past decade, microinverters have rapidly evolved, becoming a distinct category in grid-tied applications due to their advantages compared to conventional PV inverters [9, 10]. Microinverters are installed on each individual solar panel to enable panel-level efficiency optimization. While the relatively high price was initially a barrier to widespread adoption, the benefits of mass production have helped to offset this cost. Recently, single-stage soft-switching topologies with high-frequency transformers have gained popularity and are widely used in microinverter applications. Grid-connected PV systems are required to comply with stringent international standards and regulatory requirements. In many countries, galvanic isolation is mandated for distribution grid connections [3]. The large input-to-output voltage ratio to interface between a single PV module and grid presents challenges for achieving high efficiency without a transformer. Additionally, the high parasitic capacitance between the PV panel and the ground can lead to significant current leakage and potentially severe oscillations, which are also associated with electromagnetic interference (EMI) issues and safety concerns [11]. Therefore, the use of a transformer becomes almost essential for both international compliance and market viability. Power decoupling in the grid-tied inverter is necessary to compensate the mismatch between the instantaneous power of the PV panel and the AC grid, typically achieved through large power decoupling capacitors. These capacitors can be positioned either on the PV side or within the circuitry as a DC-link. The DC-link decoupling method facilitates the use of well-established control techniques in traditional circuit topologies; however, this approach typically necessitates a multi-stage structure [12]. Alternatively, four-quadrant switching circuits can be employed in a single-stage topology with a compact high frequency transformer. Recently, advanced commercial microinverters using a single-stage topology with four-quadrant switches and PV-side decoupling capacitors have gained popularity (Figure 1). This design offers a modular circuit with a simplified structure with galvanic isolation and fewer components. The use of a compact high-frequency transformer combined with four-quadrant semiconductor switches employing soft-switching techniques has become a highly attractive approach, widely adopted in commercial products in recent years [13; 14; 15].