#### The structure and design basis of LCL filter

**The structure of the LCL filter**

The filtering capability of a single inductor is limited and the volume and loss are relatively large. However, the LCL type filter has the advantages of small size and low loss, and is widely used in grid-connected inverters. The grid-connected inverter structure using LCL filter is shown in Figure 1.

It can be seen from Figure 1 that the transfer function from the output voltage u_{inv} between the bridge arms to the grid current i_{g }is:

From the perspective of amplitude characteristics, the s^{3} term can be ignored in the low frequency range. The LCL filter is equivalent to a single inductance filter with L_{1} in series with L_{2}, which is a -20dB/ten-signal frequency attenuation slope; the s term above the LCL resonance frequency can be ignored, and the amplitude-frequency characteristic curve of the LCL filter is an attenuation slope of -60dB. As shown in Figure 2, compared to the single inductance filter (shown by the dotted line in the figure, the inductance value is L_{1}+L_{2}), the LCL filter exhibits excellent high-frequency attenuation characteristics.

**Design basis of LCL filter**

Whether the parameter design of the LCL filter is reasonable affects the total volume, weight, cost and loss of the inverter, and even plays a vital role in the quality of the incoming current and the stability of the system. Generally speaking, the constraints of LCL filter parameter design include:

1. Current ripple limit on the inverter side

Generally, the inverter side current ripple ΔI_{L_1max} is required to be less than 10%~30% of the rated current Irated, namely

It should be noted that the current ripple on the inverter side generally has two considerations: one is to ensure the normal operation of the power tube, the current peak value must be less than its current allowable value; the other is that the current ripple affects the loss of the inductor on the inverter side. Considering the working reliability, there is usually a certain current margin when selecting the power tube, so the first item does not need to be specially considered. The loss of the inductor itself includes the copper loss caused by the parasitic resistance of the wire and the core loss (iron loss) caused by the high-frequency ripple current. The larger the inductance value, the smaller the current ripple and the smaller the core loss, but the copper loss increases due to the increase in the required wires; conversely, the smaller the inductance value, the smaller the copper loss, but the greater the core loss. Therefore, in the actual design, you can combine the specific magnetic core and the relevant characteristics of the wire to minimize the total loss on L_{1} by selecting an appropriate inductance value.

2. Network current ripple limit

Same as the L filter, the grid-side current of the LCL filter must also meet the relevant limits of the grid current ripple index, and the ripple content of more than 33 times should be less than 0.3% of the rated value. The 33 or more ripples of the incoming grid current are mainly located near the switching frequency, that is, the ripple near the switching frequency is required to be less than 0.3% of the current rating.

3. The total inductance voltage drop limit of the filter

Similar to the L filter, the impedance voltage drop generated by the LCL filter inductance under rated operating conditions is required to be less than 10% of the grid voltage, namely

U_{L}=ω_{0}(L_{1}+L_{2})·I_{rated}﹤10%U_{g} (1-3)

Among them, UL is the total fundamental voltage drop across inductors L_{1} and L_{2}.

4. Reactive power limit

On the one hand, in order to make the inverter bridge output power factor not too low, the capacitance value must be limited; on the other hand, the larger the capacitor value, the more reactive current will flow through the capacitor, which will increase the current amplitude on the inverter side and increase the loss, thereby affecting the efficiency of the system. Generally, it can be considered that the reactive power generated by the capacitor does not exceed 5% of the rated power of the inverter, that is

5. Resonance frequency limit

The size of the resonance frequency not only affects the current filtering effect, but also affects the design of the current control loop. Too high resonant frequency may cause excessive switching frequency ripple current, which cannot meet the requirements of relevant standards; too low resonant frequency will limit the bandwidth of the current control loop, increase the difficulty of designing the current regulator, and affect the dynamic performance of the system. Generally, the resonant frequency is selected to be greater than 10 times the fundamental frequency of the power grid and less than half of the switching frequency, namely

6. Other restrictions

Through the above restriction conditions, only the approximate value range of the LCL filter can be obtained, and the filter parameters cannot be finally determined. In the actual LCL filter design process, it is necessary to combine actual requirements to obtain optimized filter parameters suitable for practical applications. The optimization objectives that can be considered include but are not limited to: starting from saving the total inductor core material, obtaining further parameter design requirements by analyzing the relationship between the filter parameters and the switching frequency harmonic suppression and resonance frequency; the final parameter selection is based on the minimum total energy storage of the filter components as the optimization criterion; the parameters are selected for the purpose of reducing the loss of the filter or reducing the volume; and the optimization of the relationship between the parameters of the filter and the ability of the system to resist external interference (such as the background harmonics of the power grid) is considered.