## 3 Methodology
### Control  
An STPC control employs proportional-integral (PI) control and proportional-resonant (PR) control to ensure compliance with the standard values for voltage, frequency, and Total Harmonic Distortion (THD) in the PDS. Additionally, due to its control function, the STPC not only performs three-phase conversion but also provides voltage regulation. The STPC utilizes phase-by-phase control, where the single-phase input voltage and output voltage are independently regulated for each phase. Figures 6 and 7 illustrate the control block diagrams, which include DC link voltage control, DC link unbalance control, and input current control [20].  
The error is determined by setting the DC link voltage, which is the output voltage of the single-phase converter on the input side, to 750 V.  
\[e_{dc}=750V-V_{dc} \tag{3}\]  
\[I_{dc-ref}=K_{p}e_{dc}+K_{i}\int e_{dc}dt \tag{4}\]  
To determine the error, the measured \(V_{dc}\) value is subtracted from the target 750 V, and \(I_{dc-ref}\) is generated using a PI controller.  
\[H_{notch}(s)=\frac{S^{2}+w_{0}^{2}}{s^{2}{+}2\xi\omega_{0}+\omega_{0}^{2}} \tag{5}\]  
A notch filter is used to control the 2 nd to 7 th harmonic components in the output signal of the PI controller. The transfer function of the filter is as presented in Equation (5).  
\[I_{dc\_ref\_filtered}=H_{notch}(s)I_{dc\_ref} \tag{6}\]  
\[I_{d\_ref}=I_{dc\_ref\_filtered}\cdot\sin\theta \tag{7}\]  
After applying the filter, the current reference value is as in Equation (6), and to obtain the d-axis current considering the d-q coordinate system, multiply by sine as in Equation (7).  
\[I_{error}=I_{d-ref}-I_{in\_d} \tag{8}\]  
The input current \(I_{in\_d}\) is measured and subtracted from \(I_{d-ref}\).  
\[G_{PR}(s)=K_{p}+\frac{K_{r}s}{s^{2}+\omega_{res}^{2}} \tag{9}\]  
The current error is then compensated using a PR controller.  
\[V_{PR}=G_{PR}(s)\cdot I_{error} \tag{10}\]  
\[V_{final}=V_{PR}+V_{in} \tag{11}\]  
Finally, the input voltage is added, and the voltage is compared with the carrier signal to generate PWM.  
Figure 7 illustrates the output three-phase voltage control block diagram. A PR controller is utilized to regulate the output voltage and attenuate high-frequency components.  
\[V_{ref}=220\sqrt{2}\cdot\sin\theta \tag{12}\]  
\[e_{o}=V_{ref}-V_{out\_LG} \tag{13}\]  
Figure 7: Control block of output PWM.  
The difference between the target output phase voltage and the actual output phase voltage is calculated.  
\[G_{PR}(s)=K_{p}+\frac{K_{r}s}{s^{2}+\omega_{res}^{2}} \tag{14}\]  
\[V_{PR1}=G_{PR}(s)\cdot e_{v} \tag{15}\]  
A PR controller is employed to compensate for the voltage error.  
\[I_{error}=V_{PR1}-I_{out} \tag{16}\]  
\[V_{PR2}=G_{PR}(s)\cdot I_{error} \tag{17}\]  
To mitigate the voltage drop caused by the output current, the output current is measured and subtracted from the voltage controller.  
\[V_{final}=V_{PR2}+V_{phase} \tag{18}\]  
Subsequently, the output phase voltage is added, and the voltage is compared with the carrier signal to generate a PWM signal. Since the output voltage is subject to phase-by-phase control, the control process is performed phase by phase. The detailed topology of the STPC, consisting of the input and output sections, is as illustrated in Figure 8 below. Assuming a transformer as the source, a single-phase 220 V as the input voltage from the source, converted to DC through a single-phase converter, and the DC voltage is converted back to a three-phase voltage. The output voltage and THD, etc., are controlled through the control section. Since the STPC is connected not only to single-phase loads but also to multiple unpredictable single and three-phase loads, these aspects must be considered in the control strategy.