# Trajectory Control Approach for Single-Stage Soft-Switching Grid-Tied Inverters
## 2 Single-Stage Soft-Switching Module-Integrated Grid-Tied Inverters  
### The Structure of the the Single-Stage Soft-Switching Microinverter  
Figure 2 illustrates the structure of the single-stage soft-switching grid-tied inverter, which incorporates a high-frequency isolation transformer and a series resonant filter. The switching bridge connected to the DC distributed power generation, such as PV systems, is referred to as the DC side, while the bridge connected to the grid is referred to as the AC side in this paper. The DC side of the topology is implemented as a full-bridge (FB) topology using four MOSFETs (S1, S2, S3, S4) along with their body diodes, which are the two-quadrant switches depicted in Figure 3. The two-quadrant switches operate with positive voltage and allow bidirectional current flow. Switching modes are determined by the gating of the MOSFET or its body diode, based on current direction on DC side.  
The grid-side bridge structure depicted in Figure 3 adopts a half-bridge (HB) topology. The four-quadrant switch, which consists of two MOSFETs with internal diodes, is connected in series in opposite directions, is capable of blocking both positive and negative voltages while allowing bidirectional current flow. The four-quadrant switch is an essential component in advanced AC-AC conversion applications, such as matrix converters  
Figure 3: Semiconductor switch configurations.  
Figure 2: A simplified circuit structure used for the single-stage soft-switching microinverter with a high-frequency transformer and a series resonant filter.  
and microinverters (see Figure 3) [14; 15; 16; 17]. The common-source configuration, employing enhancement-mode MOSFETs and utilizing their inherent body diodes, is selected in this structure. These switches provide fully controllable turn-on and turn-off characteristics, resulting in more flexible control.  
The single-phase grid voltage \(v_{ac}(t)\) and current \(i_{ac}(t)\) are expressed as follows:  
\[v_{ac}(t)=V_{m}cos\big{(}\omega_{grid}t\big{)},\,\,\,i_{ac}(t)=I_{m}cos\big{(} \omega_{grid}t-\Phi\big{)} \tag{1}\]  
where \(\omega_{grid}\) is the grid frequency.  
The instantaneous power \(p(t)\) is expressed by Equation (2):  
\[p(t)=\frac{1}{2}V_{m}I_{m}+\frac{1}{2}V_{m}I_{m}\mathrm{cos}\big{(}2\omega_{ grid}t\big{)} \tag{2}\]  
where \(\omega_{grid}\) is the grid frequency.  
The pulsating power must be handled by PV-side decoupling capacitors. In the first and third quadrants on the \(v_{ac}\)-\(i_{ac}\) plane depicted in Figure 4, energy is transferred from the DC side to the grid, while in the second and fourth quadrants, energy flows from the grid to the DC side. When the DC side is relatively stationary at a specific operating point in steady state, the AC side operates by rotating on \(v_{ac}\)-\(i_{ac}\) plane according to the real and reactive power demands, while synchronizing with the grid frequency.  
By using a series resonance filter network and high frequency (HF) transformer, the introduced control scheme achieves zero-voltage switching (ZVS) on the DC side and zero-current switching (ZCS) on the AC side. On the DC side, switching losses are reduced through ZVS using the internal parallel diodes in the MOSFETs. On the AC side, bidirectional rectification is performed by four-quadrant switches. The HF transformer is as a key component in the circuit that delivers galvanic isolation and voltage amplification, which reduces EMI and resolves grounding issues.