# An Observer-Based Current Sensor-Less Control Scheme for Grid-Following Converters
## 6 Case Studies, Numerical Results, and Discussions  
The performance of the proposed observer and controller is evaluated through the various case studies on the sample test system in this section. The complete characteristics of the system are presented in Table 1.  
To evaluate the performance of the system under different operating conditions, different values and changes are applied to \(P_{dc}\), \(Q^{ref}\), and \(W_{c}^{ref}\). Both the actual and estimated grid-side currents, the DC-link voltage, and the active and reactive powers are presented. In addition, the system performance in the presence of uncertainty in the output filter inductance is examined. The detail of the scenarios is as follows. Initially, the values are set at \(P_{dc}=10\) kW, \(Q^{ref}=0\) kVAR, and \(V_{dc}^{ref}=750\) V. A step-up and a step-down command are given to \(Q^{ref}\), respectively. Then, a step-up and a step-down command are applied to \(V_{dc}^{ref}\), respectively. Furthermore, \(P_{dc}\) is gradually changed from 10 kW to 0 kW. While \(P_{dc}\) is 0 kW, another step-up and a step-down command is given to \(Q^{ref}\) and \(V_{dc}^{ref}\). The changes in the reference values (\(P_{dc}\), \(Q^{ref}\), and \(W_{c}^{ref}\)) are shown in Figure 6. To make the simulation tests close to the practical experimental tests, zero order hold sampling, PWM and a computation delay of \(T_{d}=1/(2f_{s})\) are also intended in the simulations. The simulation results are presented in Figures 6 and 7. Figure 6: Dynamic response of the overall system consists of (**a**) \(P_{out}\); (**b**) \(Q_{out}\); and (**c**) \(V_{dc}\) with their reference values when the observer is used in the control loop of CFL inverter. Figure 6 shows that using the proposed control scheme, including the proposed observer, DC-link voltage and \(Q_{out}\) of the GFL inverter, properly tracks their reference values with a fast dynamic response and a high stability margin. In other words, Figure 7 shows that using the observer in the control loop of the GFL inverter instead of the grid-side current measurement, does not affect the dynamic performance of the overall GFL inverter. Also, as shown in Figure 7, the estimated currents \(\widehat{t}_{d}\) and \(\widehat{t}_{q}\) are driven to their actual values very fast in startup and under the reference values variation. In addition, for better vision, the zoomed view of deriving \(\widehat{t}_{d}\) and \(\widehat{t}_{q}\) to their actual values in the startup time are shown in Figure 6c,d, which demonstrates the proper performance of the proposed observer. Moreover, to show the robustness under the presence of uncertainties, a 20% uncertainty in the output filter is considered. It is supposed that the actual \(L_{f}\) is 20% larger than the value used in the design of the observer and the control loop. In addition, as another scenario, it is supposed that the actual \(L_{f}\) is 20% smaller than the value used in the design of the observer and the control loop. The simulation results in Figure 8 show that such large uncertainties in the \(L_{f}\) value partially affect the system performance. It negligibly decreases the speed of the system in tracking the reference values of reactive power and DC-link voltage. Such minor effects can be ignored, since the important features of the system, including the tracking capability, dynamic performance, high functionality and stability margin of the system, are preserved even under the presence of the uncertainty in the model of the system. The different case studies and scenarios and the obtained results demonstrate that the proposed control scheme effectively provides proper performance even with a reduced number of measurement signals. This provides the manufacturers of the GFL inverter with an opportunity to reduce the cost and increase the reliability of the inverters by reducing the number of required sensors.