1 Introduction
Inverters based on L-type filters have a relatively simple system structure and are easier to design controllers, but the filter effect is limited. In order to reduce the harmonic content of the output current, the parameters of its current loop PI regulator must be designed very accurately. Using LCL filters can achieve better filtering effect when the inverter is connected to the grid, but the system is complex and costly.
2. Design method of LC filter
When a converter is connected to the grid for photovoltaic power generation or operates as a frequency converter to carry a load, an LC low-pass filter is often used to eliminate high-order harmonics near the switching frequency in order to reduce voltage and current output harmonics and obtain a more ideal sine wave, as shown in Figure 2-1. Generally, the cutoff frequency of the output LC filter of an SPWM inverter is much lower than the switching frequency. Research has found that selecting a filter cutoff frequency of 1/10 to 1/5 of the switching frequency has a significant attenuation effect on high-order harmonics.
When grid-connected, the filter capacitor of the LC filter can be ignored. The transfer function of its grid-connected current Igrid and the output voltage Unet of the grid-connected inverter is the same as that of a photovoltaic inverter using an L-type filter for grid connection. The smaller the LC filter capacitor C, the more negligible its influence on grid connection can be. A larger C can be used in the design, which is more beneficial for load voltage regulation, but it also draws in a larger fundamental current, which may increase the current load of the inverter. From the perspective of inverter output impedance, the inductance in the LC filter should be as small as possible, because it determines the inverter's output impedance at low frequencies. However, this will increase the harmonic current of the filter inductor, and the filter capacitor must be increased to achieve the same filtering effect.
3. LCL Filter Parameter Design
For LCL filter design and application, we can intuitively feel the advantages of LCL compared to LC through calculation, simulation and even experiments. That is, it has a better high-frequency filtering effect, and under the same conditions of filtering harmonics and lower switching frequency, the required filter inductance value of LCL is lower.
The resonant frequency of an LCL filter is denoted as fres. Because LCL filters are easily induced to resonate by high-order harmonics near the switching frequency, the resonant frequency fres should differ significantly from the switching frequency of the power devices. Generally, the resonant frequency should be less than 0.5fsw, but it cannot be too small either; otherwise, the LCL filter will amplify low-frequency harmonic currents, leading to system instability.
From the LCL circuit topology in Figure 3-1, the transfer function of the grid-side current and the bridge arm-side voltage can be calculated as follows:
As can be seen from formula (3-1) and Figure 3-2, this resonant characteristic of the LCL filter is due to the low system damping.
Since the current output from the AC grid side of the PWM converter contains a large number of harmonics, in order to avoid system resonance, the resonant frequency fres, the fundamental frequency fn, and the switching frequency generally need to satisfy the following relationship to obtain better performance:
Compared to LC filters, LCL filters change the system order from second to third, making parameter selection and design more complex. The selection of parameters for the grid-side inductor, AC-side branch capacitor, and AC-side inductor significantly impacts filtering performance and current response characteristics. Improper parameter design in LCL filters not only fails to achieve the desired filtering effect but can also distort the current and even affect the system's steady-state performance.
4. LCL Impedance Design
To increase the damping characteristics of the filter, we adopted a scheme of connecting a resistor in series on the capacitor branch, as shown in Figure 4-1.
The value of Xc can be calculated to be 0.456, which is approximately 0.5 here.
Based on the relationship between the damping resistor Rd and the capacitive reactance Xc, the parameter values of Rd are shown in Table 5-1.
Table 5-1 Rd parameter selection values
Through experimental verification, and by reverse calculation, Rd was determined. Here, Rd values were taken as 0, 0.114, 0.152, 0.301, and 0.502. Five transfer functions are listed for each of the different Rd values:
The new transfer function includes a resistance parameter Rd. By testing with different Rd values, the resonant frequency and peak amplitude of the filter can be changed, as shown in Figure 5-1. The figure shows that if the bandwidth includes the cutoff frequency or frequencies near it, adding a damping resistor needs to be considered.
When considering the damping resistor, the selection of its parameters needs to take into account the inductive reactance ratio matching between L and Lg. Furthermore, as shown in Figure 1, increasing Rd weakens the oscillation peak, but also reduces the gain attenuation. The figure shows that the compatibility between the oscillation peak and gain attenuation is best when Rd = 0.114Ω and 0.152Ω.
6 Conclusions
From the perspective of damping characteristics, the transfer function exhibits a resonant peak without a damping resistor; however, with the addition of a damping resistor, the resonant peak gradually attenuates as its value increases. Looking at the transfer characteristics across the entire frequency range, while the addition of the damping resistor does not change the high-frequency attenuation characteristics, it significantly alters the system's low-frequency characteristics. Specifically, the transfer ratio of the bridge arm voltage to the grid-side current decreases with increasing damping resistor value, which affects the system's control performance. When selecting the damping resistor R, we must consider two points:
1. The resonant peak value should be as small as possible;
2. Minimize low-frequency harmonic attenuation as much as possible;
Considering both of the above points, the optimal Rd value is selected. Of course, in the experiment, if such resonance occurs, the R value needs to be adjusted according to the specific situation, and the experimental effect needs to be observed before a decision can be made, because parasitic parameters in the system loop are not taken into account.
