## 2 Large-Signal Model of Q1S AC-DC Converter  
For the purpose of analyzing the influence of grid voltage low-order harmonics on grid currents, the large-signal model of the Q1S AC-DC converter under ITPS is built. Figure 1 shows the topology structure of the Q1S AC-DC converter, which is comprised of the front-end synchronous rectifier and the back-end DAB converter. Its front-end synchronous rectifier converts the grid voltage to the unipolar rectified waveform. Comprised of the DC side capacitor \(C_{1}\) and AC side inductor \(L_{g}\), the LC filter can filter out the high-frequency current components before they flow into the grid. Thus, the capacitance of  
\(C_{1}\) is generally very small and not exceeding tens of micro-Farad. HB1 and HB2 represent two H-bridge converters. \(v_{p}\) and \(v_{s}\) are the high-frequency voltages of HB1 and HB2. \(v_{dc1}\) and \(v_{dc1}\) are DC side voltages, and \(i_{dc1}\) and \(i_{dc2}\) are DC side currents. \(i_{p}\) represents the primary current of the high-frequency transformer (HFT). The turns ratio is \(n\). After the grid voltage is rectified, the unipolar voltage \(v_{dc1}\) can be acquired on \(C_{1}\). The expression is shown as  
\[v_{dc1}=V_{m}|\sin(\omega_{1}t)| \tag{1}\]  
In (1), \(V_{m}\) and \(\omega_{1}\) represent amplitude and frequency of the grid voltage. For the purpose of keeping sinusoidal grid current \(i_{g}\), the expected average DC side current of HB1 in the switching cycle \(\langle i_{dc1}\rangle_{T_{S}}^{*}\) should be sinusoidal. As reported in [17], its definition is  
\[\langle i_{dc1}\rangle_{T_{S}}^{*}=I_{m}^{*}|\sin(\omega_{1}t)| \tag{2}\]  
In (2), \(I_{m}^{*}\) is the expected AC side current amplitude of this converter. Since the grid frequency is far less than DAB converter's switching frequency, \(v_{dc1}\) can be deemed a constant. Thus, at the switching cycle scale, the principle of the DAB converter put behind and exhibited in Figure 1 identifies with the routine DAB DC-DC converter. Then this converter can realize the function of AC-DC buck-boost voltage conversion and bidirectional power flow. In [17], an ITPS modulation strategy is proposed to completely eliminate the circulating current and make transformer currents uncoupled in adjacent switching cycles, thus realizing the AC side transfer current's accurate control of the converter. Switching period scale operating waves of the ITPS put forward in [17] are shown in Figure 2. In Figure 2, the voltage conversion ratio is \(k=v_{dc1}/nV_{dc2}\), \(\langle i_{dc1}\rangle_{T_{S}\_{c}\_{c}\_{c}\_{c}\_{c}}=\frac{v_{dc1}T_{S}}{4 l_{\text{init}}}\frac{k-1}{k^{3}}\). \(D_{1}\) and \(D_{2}\) represent the internal phase angles of HB1 and HB2, while \(D_{\phi}\) represents the outer phase shift angle. From Figure 2, transformer currents of the contiguous switching cycles are decoupled and waveforms of the positive half switching cycle and the negative half switching period  
Figure 1: Schematic of Q1S AC-DC converter. are completely symmetrical. For the sake of the simplification, the large-signal model is derived based on the waveforms in the positive half switching period. From Figure 1, the grid side filter inductor, capacitor, and transformer leakage inductor are energy-storage components in this converter. Therefore, \(i_{g}\), \(v_{dc1}\) and are selected as the state variables for the large-signal model building of this converter. Based on Figures 1 and 2a, the state equation \(i_{p}\) during \(t\in[t_{0},t_{3})\) is expressed as (3) in [17]. \[\frac{\mathrm{d}i_{p}}{\mathrm{d}t}=\frac{v_{p}-nv_{s}}{L_{leak}}= \begin{cases} \frac{v_{dc1}}{L_{leak}},&[t_{0},t_{1})=D_{\varphi}\frac{T_{S}}{S}\\ \frac{v_{dc1}-v_{dc2}}{L_{leak}},&[t_{1},t_{2})=\left(1-D_{1}-D_{\varphi}\right) \frac{T_{S}}{2}\\ \frac{-nv_{dc2}}{L_{leak}},&[t_{2},t_{3})=D_{1}\frac{T_{S}}{2}\end{cases}