# Analysis and Optimization of Output Low-Pass Filter
## 4 Design Trade-Offs
### Effect of Cn Variation  
The design regions shown in Figure 14 indicate a capacitance of 0.12 pu, enabling the filter to function at 20% of its rated power while achieving a 0.8 leading power factor. Furthermore, this arrangement restricts the value of \(L_{n}\) to a limited range, as shown in Figure 13. This limited range is advantageous as bigger capacitors are typically more economical and easier to find on the market than large inductors. The allowable range of \(L_{n}\) may be increased by decreasing the capacitance value \(C_{n}\) if required. However, it is critical to realize that this reduction would lead to an increase in \(Z_{0n}\). This trade-off emphasizes the importance of strategically selecting component values to obtain maximum performance while balancing cost and availability. As a result, when designing the filter, it is critical to carefully analyze both capacitance and inductance values to ensure efficiency and compliance with system specifications.  
Using the chosen baseline filter parameters from Section 4, Figure 18a shows how the CSI's output current's THD is related to output power for different \(C_{n}\) values, taking into account different levels of irradiance. Although the THD values at the rated power are similar across the different configurations, the case with a capacitance of 0.05 pu exhibits the lowest THD overall. The grid's THD requirements are met for \(C_{n}\) values between 0.05 and 0.15 pu at the rated output power. On the other hand, the THD shows an inverse relationship with \(C_{n}\) in medium to low irradiation conditions, which is especially clear in cases with smaller capacitance values. This means that under less optimal irradiation conditions, a drop in capacitance corresponds with a rise in THD.  
Figure 17: CL filter flowchart for determining filter parameters.  
In order to maintain a consistent cutoff frequency for lower values of \(C_{n}\), the corresponding value of \(L_{n}\) must be adjusted, which raises the characteristic impedance \(Z_{0}\). As can be seen in Figure 18c, an increase in \(Z_{0}\) will cause a large increase in \(P_{d}\) as the power dissipation \(P_{d}\) is directly proportional to \(Z_{0}\). This relationship shows the requirement of carefully selecting capacitance and inductance values to minimize power losses and achieve higher efficiency. The increase in characteristic impedance due to higher inductance requires consideration of its effects on power dissipation, since these can affect the overal efficiency and thermal management of the system [41]. Consequently, to have a better performance and efficiency from a CL filter it is important to analyze these dynamics.  
Raising the capacitance \(C_{n}\) to a value exceeding 0.12 pu may not ensure that the power factor remains above 0.8 when operating at 20% of the rated power, as illustrated in Figure 18b. Nevertheless, the power factor curve corresponding to \(C_{n}\) = 0.15 pu is close to achieving a power factor of 0.8 at that output level. The increase in the capacitance could affect the power factor. Therefore, this shows \(C_{n}\) should be carefully selected to operate efficiently at lower power levels. This also indicates that optimizing the parameters is very important to achieve the desired operational conditions.