## 3 Smart Inverter Control Architecture
### Output Power Control of a Three-Phase System  
Reference [20] not only proposed the intelligent MPPT technology for PVMA but also engaged in the regulation of the output real power and reactive power of a single-phase smart inverter. However, the phase angle of the output voltage was detected by a sensor. The MPPT method of PVMAs is not the main focus of this paper. In this paper, we mainly regulate the output real power and reactive power of three-phase smart inverters to maintain the supply voltage of the grid system. To simplify the control complexity, we convert the coordinates of a three-phase to two-phase system of voltage, and estimate the phase angle of the grid voltage using the phase-locked loop (PLL) system based on the  
Figure 6: Control architecture of DC-link voltage. second-order generalized integrator (SOGI). Then, the estimated phase angle is substituted into [PERSON]'s coordinate conversion matrix to convert the coordinates of the three-phase to two-phase voltage, so the installation of the phase sensor can be avoided. Should the output of the grid-connected system for the three-phase inverter be a three-phase balanced system, the phases between the voltages or currents of the three-phase output differ by \(120^{\lx@math@degree}\). Generally, [PERSON]'s transformation matrix [21; 22] can be utilized to convert the _abc_ axial vectors of the inverter into _dq_ axial vectors for control. When analyzing the real and reactive powers of the three-phase system, the three-axial vector must also be converted into a two-axial vector DC system for calculation, which projects the _abc_ three-phase stationary coordinates of the inverter to the \(\alpha\beta\) stationary coordinates. The equation can be expressed as Equation (16). \[T_{abc/\alpha\beta}=\frac{2}{3} \begin{bmatrix}1&\frac{-1}{2}&\frac{-1}{2}\\ 0&\frac{\sqrt{3}}{3}&\frac{-\sqrt{3}}{2}\\ \frac{1}{2}&\frac{1}{2}&\frac{-1}{2}\end{bmatrix}  \tag{16}\]  
Consequently, the \(\alpha\beta\) stationary coordinates are converted to the _dq_ synchronous rotating coordinates matrix. The equation can be expressed as Equation (17). \[T_{\alpha\beta/dq}=\frac{2}{3} \begin{bmatrix}\cos\theta&\sin\theta&0\\ -\sin\theta&\cos\theta&0\\ 0&0&1\end{bmatrix}  \tag{17}\]  
Among them, \(\theta\) is the rotating angle of coordinates. Generally, \(\theta\) is the phase of mains voltage, which makes the rotating angle of coordinates at the same phase as the mains voltage. Based on Equations (16) and (17), it is known that the conversion matrix for converting _abc_ three-phase stationary coordinates to _dq_ synchronous rotating coordinates is shown in Equation (18). \[T_{abc/dq}=\frac{2}{3} \begin{bmatrix}\cos\theta&\cos(\theta-\frac{2\pi}{3})& \cos(\theta+\frac{2\pi}{3})\\ -\sin\theta&-\sin(\theta-\frac{2\pi}{3})&-\sin(\theta+\frac{2\pi}{3})\\ \frac{1}{2}&\frac{1}{2}&\frac{1}{2}\end{bmatrix}  \tag{18}\]  
The block diagram for the phase estimation using a second-order generalized integrator (SOGI)-based phase-locked loop (PLL) system [23; 24] is shown in Figure 7. Consequently, the phase estimated \(\theta\) is fed back to the coordinate conversion matrix in Equation (18). Where the constants of the P-I controller were \(K_{Po}\) = 100 and \(K_{fo}\) = 50,000, respectively. After calculating the real and reactive power of inverter output, where errors were generated by comparing the command values of real power and reactive power, the direct axis current command \(I_{d}^{*}\) and quadrature axis current command \(I_{q}^{*}\) of the synchronous coordinates were obtained via the P-I controller. Consequently, the phase angle \(\theta_{vi}\) difference between voltage and current could be calculated from Equation (19), where Figure 8 displayed the control architecture for the phase angle of a smart inverter [18]. In Figure 8, the proportional and integral constants of the P-I controller for real power were set as  
Figure 7: Block diagram for phase estimation using a SOGI-based PLL system.