#### Overview of the network filter and the parameter design of L filter

**Overview of the network filter**

The PWM modulation of the grid inverter leads to a large number of switching frequency and its multiplier harmonic voltages in the output voltage of the bridge arm, and finally leads to corresponding harmonic currents in the grid current. However, in order to make the grid-connected inverter friendly to the grid, the harmonic content in the grid-connected current of the grid-connected inverter is strictly limited. In order to meet the requirements of harmonic current suppression for switching frequency and its doubling frequency, the grid filter must be selected and designed reasonably. From the perspective of improving the conversion efficiency of the inverter as much as possible, the impedance of the grid filter is required to be small. This can only be achieved by increasing the attenuation gain of the grid filter in the high whisker section. Therefore, the use of the L filter is limited, and the third-order LCL filter can meet the above requirements. However, the first problem encountered in the application of the LCL filter is the design and optimization criteria of the filter component parameters. In other words, the single L filter is a first-order system, with simple structure and design, and easy to control, but its ability to suppress high frequency harmonics is poor, and the filter inductance required to meet the grid current standard is relatively large; the LCL filter is a high-end system with good high-frequency attenuation characteristics. Compared with a single L filter, its volume, weight, cost, and loss are greatly reduced, but its parameter design is more complicated. In addition, in order to further reduce the volume and weight of the filter, higher-order LLCL filters have also received extensive attention. The LLCL filter essentially uses the LC trap to replace the capacitor in the original LCL filter to achieve better switching frequency harmonic suppression and reduce the grid-side filter inductance. The following article will analyze the above three types of filters (including L filter, LCL filter and LLCL filter), list the design basis of each type of filter, give design examples, and analyze the filtering performance of each type of filter.

**L filter and parameter design**

1. L filter structure

The structure of the grid-connected inverter using single inductance filtering is shown in Figure 1. Among them, U_{dc} is the DC side voltage; U_{g} is the grid voltage; L is the filter inductance; i_{g} is the grid current.

It can be seen from Figure 1 that when a single inductance filter is used, the transfer function of the output voltage u_{inv} to i_{g} between the bridge arms is

Figure 2 shows the amplitude-phase characteristic curve of the transfer function of formula (1.1). It can be seen that in the logarithmic frequency coordinate, the filtering characteristic of a single inductance filter is a -20dB/ten-signal frequency range diagonal line.

2. Design basis

The L-type filter contains only one inductor, with fewer design constraints and a simpler process.

(1) Ripple limit of incoming current

Grid-connected inverters with single-inductor filtering have limited filtering capabilities. It is difficult to make the grid-connected current ripple meet relevant restrictions, especially if the ripple content of 33 times or more should be less than 0.3% of the rated value. If designed under this condition, the inductance value will be very large. On the one hand, the excessive inductance will cause the filter volume and weight to be too large, and on the other hand, it will affect the dynamic response of the system. Therefore, the design of a single inductance filter often only considers suppressing the ripple of the incoming grid current to 10% to 20% of the rated current to ensure a certain filtering effect. It is difficult to attenuate the sub-harmonics of the switching frequency by relying solely on inductance. This filter structure is more common in practical applications where transformers are used.

(2) Filter inductor voltage drop limit

The fundamental wave voltage drop of the filter inductor increases as the current increases. In order to avoid over-modulation to ensure the normal operation of the inverter, it is often required that the total voltage drop on the filter inductance under the rated current is less than 10% of the grid voltage, that is

U_{L}=ω_{0}·L·I_{rated}﹤10%U_{g} (1.2)

3. Design Examples

A 5kW single-phase full-bridge grid-connected inverter with unipolar SPWM strategy is selected as the object, and the filter parameters of the grid-connected inverter are designed as examples.

(1) Consider the grid current ripple limit

Considering the unipolar SPWM strategy, assuming that the on-time in a switching cycle is D(t)Ts, the grid current ripple pulsation satisfies:

Among them, D(t) is the duty cycle in a certain switching period, and T_{s} is the switching period. For the unipolar SPWM strategy, the duty cycle D(t) satisfies:

D(t)=Msin(ω_{0}_{ }t) (1.4)

Among them, M is the modulation ratio.

Considering the existence of a phase-locked loop when grid-connected, the modulation wave is approximately in phase with the grid voltage, so the DC side voltage U_{dc} and the grid voltage U_{g} approximately satisfy:

U_{g} =U_{dc} Msin(ω_{0}_{ }t) (1.5)

Therefore, the further expression of the grid current pulsation is:

From equation (1.6), it can be seen that the lower limit of the inductance can be obtained according to the grid current ripple limit:

Finally, according to the working parameters of the inverter, considering that the ripple current ripple is 15% of the rated value of the grid current, the inductance value must meet Lg﹥1.38 mH.

(2) Consider the limit of the total inductance voltage drop of the filter

Generally, the voltage drop U_{L} generated by the inductance is required to be less than 10% of the rated value of the grid voltage U_{rated}, which can be obtained by formula (1.2):

The value range of L can be obtained from the above formula:

Bring in relevant data and calculate L<1.74mH.

Combining the above two restriction conditions, considering that the smaller the ripple of the incoming grid current, the better the quality of the incoming grid current, so the inductance value of the single-inductor filter takes its upper limit value of 1.74mH.