## 2 Proposed SST Circuit, Specifications and Control Layout
### Control Layout of the SST-Voltage Source Converter  
Flux-oriented vector current control (VOC), based on two control layers: Outer current control layer (OCC) and inner current control layer (ICC), was used to control the operation of voltage source converters (VSCs) [23]. The outer layer satisfied the DC voltage, active power and reactive power demands of the VSCs while the inner layer used the decoupling control method to regulate the q-axis and d-axis currents. Both control loops had a proportional and integral (PI) controller as a common element in them. DC link voltage \(V_{DC,\mathit{mes}}\) was regulated using the voltage droop control [24]. Through the investigation of the bi-layer control architecture deployed within a multi-input multi-output (MIMO) voltage source converter, it can be realized that the operation of SST-VSC becomes a bit complex [25]. This complex control architecture has many variables, which need to be controlled precisely using PI controllers [26]. Therefore, it is the requirement of the system that PI controllers should be optimally tuned to provide both transient and steady state desired responses. However, tuning PI parameters of the nonlinear system like the voltage source converter, is a challenging task within itself [27]. Vector current control was used at the point of common coupling, which regulates the DC voltage control at VSC and power flow control with ac voltage regulation [28]. In this technique, ac voltage  
Figure 1: Proposed circuit diagram of the solid-state transformer. and current of the VSC were converted into a rotating d-q reference frame, which was synchronized with ac grid voltages using a phase locked loop (PLL). This methodology not only regulated DC and ac voltage but also provided the decoupled control of both active and reactive power. The layout of the d-q control architecture-based SST-VSC is shown in Figure 2. The outer control loop produced reference currents for the inner current loop, which then provided the reference voltage for the d-q reference frame. By taking the d-q control frame into consideration, the internal control loop used the PI controllers, which generated the reference current and maintained the required voltage for the VSCs. Voltage expression at the point of common coupling (\(p_{c}\)) and the voltage source converter side (\(v_{s}\)) can be given as:  
\[e_{C}-v_{S}=\ R\times i_{S}\ +\ L\ \frac{di_{S}}{dt}, \tag{1}\]  
where \(R\) and \(L\) represent the resistance and inductance between SST-VSC and point of common coupling (PCC), while \(i_{S}\) is the current from the grid to the SST-VSC. From Park's transformation:  
\[e_{d}-v_{d}=\ Ri_{d}\ -\ \omega Li_{q}\ +\ L\ \frac{di_{d}}{dt}. \tag{2}\]  
\[e_{q}-v_{q}=\ Ri_{q}\ +\ \omega Li_{d}\ +\ L\ \frac{di_{q}}{dt}. \tag{3}\]  
Here \(\omega\) represents the angular frequency at the PCC of ac system. Based on (2) and (3), the ICC control layout is shown in Figure 3. The reference signals (\(V_{d\_ref}\) and \(V_{q\_ref}\)) were transformed back to the _abc_ frame, which were used to generate switching pulses for IGBTs of VSC. In this research, the classical tuning method was used to tune the PI controller parameters. The transfer function of the simple PI controller is:  
\[F(s)\ =k_{p}\ +\ \frac{k_{i}}{s}. \tag{4}\]  
Figure 2: The d–q control architecture of solid state transformers-voltage source converters (SST-VSC). According to internal model control (IMC) method as presented in [29], we can write:  
\[F(s)\,=\,k_{p}\,+\,\frac{\alpha_{ICC}}{s}\,\widehat{G}^{-1}\,(s)\,=\,\frac{\alpha _{ICC}}{s}\,(R\,+\,sL).\]  
\[F(s)\,=\,\alpha_{ICC}\,L\,+\,\alpha_{ICC}\,\frac{R}{s}. \tag{5}\]  
Here \(\alpha_{ICC}\) (rad/s) represents the bandwidth of the current controlled system; \(\widehat{G}(s)\) is the estimation of \(G(s)\). Comparison of (4) and (5) yields the range of PI controller coefficients for ICC as:  
Figure 2.0  
Figure 2.1  
The bandwidth \(\alpha_{ICC}\) for the ICC must be selected such that it is ten times lesser than the switching frequency [30; 31].