### Structure of the Three-Phase Grid-Connected Inverter Based on an LCL Filter and Active Modeling  
Figure 1 shows the block diagram of the current-controlled grid-connected VSI in the dq synchronous reference frame (SRF). The terminal of the inverter uses a third-order LCL filter to fade the switch harmonics injected into grids. The PLL provides the reference phase as well as the frequency of the grid voltage at the node of the public coupling for operating the dq transformation. If using a DC power source powers the voltage source converter of Figure 1, then there is no need for a controller to regularize the voltage of the DC link. (OR, the system requires another one to modulate the voltage of the DC link and accordingly produce the d-axis current reference). Generating the LCL filters in a \(dq\) SRF shows Formulas (1)-(3) below:  
\[L_{g}\frac{d_{g}^{dq}}{dt}=v_{g}^{dq}-v_{C}^{dq}-\left(r_{g}+j\omega L_{g} \right)_{c}^{dq} \tag{1}\]  
\[C_{f}\frac{dv_{C}^{dq}}{dt}=i_{g}^{dq}-i_{C}^{dq}-j\omega C_{f}v_{C}^{dq} \tag{2}\]  
\[L_{C}\frac{d_{\mathrm{inv}}^{dq}}{dt}=v_{C}^{dq}-v_{\mathrm{inv}}^{dq}-(r_{C}+ j\omega L_{C})_{c}^{dq} \tag{3}\]  
Figure 1: Three-phase Inverter based on an LCL filter. In expressions, \(r_{g}\) and \(r_{c}\) represent the equivalent series resistances of the grid-side and converter-side inductances, respectively. also \(I_{g}-I_{g1}+I_{g2}\). Figure 2 gives the Bode curve of the transferring function according to equations. As shown in this plot, there is a significantly sharp resonance peak value at the resonance frequency actively or passively damped. Because the passive damping method decreases the whole system's efficiency and involves an additional power fading loss, so the active damping way is highly recommended. Another problem that affects the stability of the current controller is the existence of grid disturbances. A not great level of value of the harmonic distortion in grid voltage may markedly increase the THD (Total Harmonic Distortion) of the injected current and finally cause system instability owing to some probable interactions between the distributed generating interface and the grid disturbances. Consequently, the high rejecting capability of the grid disturbance depicts one of the significant characteristics regarded in a current controller in some grid connection applications. Figure 3 illustrates the architecture of the first-order ADRC. This structure consists of two main control loops. The inner loop, the disturbance rejection loop, compensates for all disturbances. The effectiveness of this control loop relies on the accuracy of the estimated total interference through the Linear Extended State Observer (LESO). The outer loop, a feedback control loop, achieves the desired signals using a specific feedback controller. Figure 3: Three-phase Inverter based on an LCL filter. Figure 2: Three-phase Inverter based on an LCL filter. Think about following an \(n\)th-order plant with a single output \(y\) and a single input \(u\):  
\[y^{n}(t)=f\Big{(}y^{(n-1)},y^{(n-1)},\cdots,y(t),w(t)\Big{)}+bu(t) \tag{4}\]  
In this context, \(w\) represents the internal disturbances, including parameter uncertainties and unmodeled dynamics, while \(b\) is a given constant. The function \(f\), expressed as \(f\Big{(}y^{(n-1)},y^{(n-1)},\cdots,y(t),w(t)\Big{)}\), describes the overall dynamics of the unknown plant. Consequently, an accurate model of this plant is not available. ADRC offers a specialized technique to address this type of problem. Unlike conventional control methods that rely on explicit modeling of the plant, ADRC serves as an alternative approach that significantly reduces the system's dependence on an accurate model. Designing a current controller for a third-order LCL filter poses a challenging problem. Simplifying the high-order transfer function using low-order models is often beneficial in designing and analyzing control systems. A low-order ADRC controller is commonly selected for this purpose.