# Analysis and Optimization of Output Low-Pass Filter
## 6 Conclusions  
The high-frequency PWM harmonics generated by a current-source grid-connected inverter are eliminated by a capacitive-inductive low-pass grid filter, designed based on impedance mismatch criteria. The analysis of this filter indicates that incorporating damping is crucial to mitigate the effects of resonance. This study explored four different configurations for placing the damping resistor and investigated the corresponding tradeoffs involved between power loss and harmonic attenuation, focusing on the THD of the output current. The optimal design, which efficiently minimized power loss while attenuating high-frequency PWM harmonics, was identified as the configuration where the damping resistor was placed in parallel with the filter inductor. Furthermore, the study highlighted that selecting the filter's capacitance and inductance required balancing between the grid's power factor and the cutoff frequency, demonstrating the importance of strategic component selection in optimizing filter performance and ensuring effective harmonic suppression.  
A detailed filter design procedure was developed to determine the filter parameters according to the specified cutoff frequency, power loss, and optimal output current THD. Baseline values for the filter parameters were set to \(C_{n}\) = 0.1 pu, \(f_{c}\) = 500 Hz, and \(Q\) = 4. This filter was used to analyze the impact of a non-linear PV array current on the CSI output. Parameter optimization occurred within defined limitations. The analysis revealed that a low cutoff frequency (\(f_{c}\)\(\leq\) 250 Hz) may not meet the grid's THD and PF requirements. Additionally, a low quality factor (\(Q\) < 2) and a high capacitance value (\(C_{n}\) > 0.15 pu) may not meet grid standards for THD and PF. The designed low-pass filter met the grid's THD and PF requirements while producing less power loss.  
Using two prototypes, the experiments confirmed that the design approach was practically effective. The power factor consistently remained within acceptable limits. The THD results showed a significant reduction; however, they slightly exceeded the 5% limit as defined in [11]. This shows that the inverter system will need an improved control algorithm in parallel with the CL filter design procedure to maintain the THD standard while maintaining efficiency. Despite this limitation, the CL filter design methodology presented in this study offers a structured approach for efficiently determining and implementing into practice the ideal values of the inductance (\(L\)), capacitance (C), and damping resistance (\(R_{D}\)).  
Conceptualization, G.E. and D.M.W.; methodology, G.E. and D.M.W.; software, G.E. and D.M.W.; validation, G.E. and D.M.W.; formal analysis, G.E. and D.M.W.; investigation, G.E. and D.M.W.; resources, G.E. and D.M.W.; data curation, G.E. and D.M.W.; writing--original draft preparation, G.E. and D.M.W.; writing--review and editing, G.E. and D.M.W.; visualization, G.E. and D.M.W.; project administration, G.E. and D.M.W. All authors have read and agreed to the published version of the manuscript.  
This research received no external funding.  
Figure 23: Measurement of the (**a**) output current with its (**b**) FFT spectrum. The output filter configuration is FC 3.