## 3 Disturbance Rejection Control of GCI Current Control Systems  
In a GCI current control system, grid voltage is regarded as disturbance. When grid faults occur, overcurrent damages the system or its electrical circuits. One approach to solving this problem is designing a system that directly rejects any disturbances. Direct disturbance rejection control (DRC) can be achieved by feedforwarding a signal with the opposite polarity of the grid voltage to the GCI system. DRC can be implemented using grid voltage measured by a voltage sensor or by relying on a grid voltage observer. Voltage sensors are simple to implement, but their use comes at the cost of increased of system expense, complexity, and volume. For that reason, our proposed GCI current control algorithm relies on grid voltage estimates by a grid voltage observer. For a properly developed grid current observer, the controller output of the grid current observer will be identical to the grid voltage. Estimated grid voltage can be used not only to implement DRC, but also to cancel the harmonics in voltage, in the event the actual grid voltage includes harmonic components. Ultimately, total harmonic distortion (THD) can be reduced, and power quality can be improved. The proposed GCI current control system with DRC using a grid current observer is shown in Figure 5.  
Figure 4: Frequency response of the GCI current control system with and without the CFFC.  
The main objective of the DRC is to improve the GCI's resilience against disturbance. Dynamics stiffness--the amount of disturbance required to change an output signal--is one metric for evaluating system robustness. Systems with higher dynamics stiffness are more robust. Dynamic stiffness transfer functions of the GCI system are derived in Equations (6) (with the DRC) and (7) (without the DRC).  
\[\frac{\mathrm{v}_{\mathrm{g}}}{\mathrm{i}_{\mathrm{g}}} =\frac{L_{1}\cdot L_{2}\cdot C_{\mathrm{f}}\ast^{4}+R_{\mathrm{d} }\cdot C_{\mathrm{f}}(L_{1}+L_{2})\cdot\mathrm{s}^{3}+(L_{1}+L_{2}+R_{\mathrm{ d}}\cdot C_{\mathrm{f}}\cdot K_{\mathrm{p}})\cdot\mathrm{s}^{2}+(L_{1}+L_{2}+R_{ \mathrm{d}}\cdot C_{\mathrm{f}}\cdot K_{\mathrm{p}})\cdot\mathrm{s}^{2}+(K_{ \mathrm{p}}+R_{\mathrm{d}}\cdot C_{\mathrm{f}}\cdot K_{\mathrm{i}})\cdot \mathrm{s}+K_{\mathrm{i}}}{L_{1}\cdot C_{\mathrm{f}}\mathrm{s}^{3}+R_{ \mathrm{d}}\cdot C_{\mathrm{f}}\cdot\mathrm{s}^{2}+\mathrm{s}} \tag{6}\] \[\frac{\mathrm{v}_{\mathrm{g}}}{\mathrm{i}_{\mathrm{g}}} =\frac{L_{1}\cdot L_{2}\cdot C_{\mathrm{f}}\ast^{4}+R_{\mathrm{d} }\cdot C_{\mathrm{f}}(L_{1}+L_{2})\cdot\mathrm{s}^{3}+(L_{1}+L_{2}+R_{\mathrm{ d}}\cdot C_{\mathrm{f}}\cdot K_{\mathrm{p}})\cdot\mathrm{s}^{2}+(K_{\mathrm{p}}+R_{ \mathrm{d}}\cdot C_{\mathrm{f}}\cdot K_{\mathrm{i}})\cdot\mathrm{s}+K_{\mathrm{ i}}}{L_{1}\cdot C_{\mathrm{f}}\mathrm{s}^{3}} \tag{7}\]  
Figure 6 graphically illustrates the frequency response of the dynamic stiffness of the GCI system as derived from Equations (6) and (7).  
As shown in Figure 6, dynamics stiffness (resilience) of the GCI current control system is significantly improved with the DRC, especially at low and medium frequency range. The DRC's effectiveness is further verified using simulations and experiments in the subsequent sections.  
Figure 5: System block diagram with a grid current observer for disturbance rejection in a GCI current control system.  
Figure 6: Dynamic stiffness of the GCI current control system with and without the DRC.