## 3 Influence of Grid Harmonics on Grid Currents  
From Figure 1, the actual grid currents are decided not only by grid voltages but also by AC side average currents of the converter. For this part, taking the low-order grid voltage harmonics into consideration, the influence of these harmonics on grid currents is researched based on the built model.  
Based on the principle of ITPS in [17], AC side currents of the converter are still sine shaped even if there are low-order harmonics in grid. From its large-signal model, the converter under the ITPS can be equivalent to a controlled current source \(i_{av1\_u}\). Then when there are low-order harmonics in grid, the fundamental and harmonics equivalent circuits of this Q1S AC-DC converter are shown as Figure 4a,b, respectively.  
From the fundamental equivalent circuit in Figure 4a, the relationship among various variables yields  
\[\left\{\begin{aligned} & i_{g1}=i_{C_{1}1}+i_{av\_u1}\\ & i_{C_{1}1}=j\omega_{1}\mathrm{C}_{1}\cdot y_{dc1\_u}\\ & v_{dc1\_u}=u_{g1}-j\omega_{1}L_{g}\cdot i_{g1}-r_{L}i_{g1}\end{aligned}\right. \tag{13}\]  
Figure 3: Bode diagrams and simulation data of various transfer functions.  
From (13), the grid current fundamental component is  
\[i_{\text{gl}}=\frac{j\omega_{1}C_{1}u_{gl}+i_{\text{avl},\text{\_u1}}}{\left(1+j \omega_{1}C_{1}r_{L}-\omega_{1}^{2}L_{g}C_{1}\right)} \tag{14}\]  
From the harmonics equivalent circuit in Figure 4b, the grid current harmonics yield  
\[i_{\text{gh}}=\frac{u_{gh}}{j\omega_{h}L_{g}+1/(j\omega_{h}C_{1})+r_{L}i_{ \text{g}1}}=\frac{j\omega_{h}C_{1}u_{gh}}{\left(1+j\omega_{h}C_{1}r_{L}-\omega_ {h}^{2}L_{g}C_{1}\right)} \tag{15}\]  
From (14) and (15), the expression of the total grid current yields  
\[\begin{array}{ll}i_{\text{g}}&=i_{\text{gl}}+i_{\text{gh}}\\ &=\frac{j\omega_{1}C_{1}u_{gl}+i_{\text{ext},\text{\_u1}}}{\left(1+j\omega_{1} C_{1}r_{L}-\omega_{1}^{2}L_{g}C_{1}\right)}+\frac{j\omega_{h}C_{1}u_{gh}}{ \left(1+j\omega_{h}C_{1}r_{L}-\omega_{h}^{2}L_{g}C_{1}\right)}\end{array} \tag{16}\]  
From (16), \(i_{\text{g}1}\) is mainly determined by the currents of the converter AC side, while grid voltage low-order harmonics generate grid current harmonics, whose amplitudes are related to the LC filter parameters. The orders of those harmonics are consistent.  
The effect of LC filter parameters on grid current low-order harmonics is analyzed as follows. For the parameter design of the LC filter, the ranges of the LC filter parameters should be comprehensively determined by the filter cutoff frequency, filter damping, and the power factor, and the specific parameters are finally determined according to the actual system operation performance [21]. Hence, for a certain filter resonant frequency, there are a series of LC filter parameters to be selected. Figure 5 shows the simulation waveforms of grid currents with two different groups of the filter inductance and capacitance, while with the same resonant frequency of 5 kHz. The simulation parameters of the converter are shown in Table 1. The 3 rd and 5 th harmonics contents in the grid voltage are 10% and 5%, respectively, and the given grid current amplitude is 5A.  
Figure 4: AC side equivalent circuits of QIS AC-DC converter. (a) The fundamental equivalent circuit, (b) the harmonic equivalent circuit.  
Figure 5: Simulation waveforms with different filter parameters. (a,c) 120 uH & 7.5 uF and FFT of ig, (b,d) 180 uH & 5 uF and FFT of ig.  
In Figure 5, under two groups of LC filter parameters, the THDs of grid currents are all greater than 5% and the grid currents contain considerable 3 rd and 5 th harmonics. It follows that the grid voltage low-order harmonics will cause the same order grid current harmonics. Figure 5 can also illustrate that only varying the parameters of the filter is not a highly efficient approach to eliminate the grid current harmonics caused by the grid harmonics. Therefore, for the purpose of eliminating the influence of grid harmonics on grid currents, it is necessary to research a new closed-loop control strategy of grid currents.