# Output Filter Design for a Novel Dual-Input PV-Wind Power Converter by Energy Balance Principle
## 3 Operation Principle  
The operation of the DIPWC can be divided into six stages. Figure 2 shows the related equivalents, while corresponding key waveforms are depicted in Figure 3. In Figure 1, the magnetizing inductances,  
Figure 1: The configuration of the presented dual-input photovoltaic-wind converter (DIPWC). \(L_{m,wind}\) and \(L_{m,pv}\), are both in CCM. To simplify the circuit analysis, there are some assumptions made in the following. 1. In Figure 2, capacitances of \(C_{1,wind}\), \(C_{2,wind}\), \(C_{1,pv}\), and \(C_{2,pv}\) are large enough so that all the voltages across them can be regarded as constant in a switching cycle. 2. The internal resistances and parasitic capacitances in all active switches are neglected. 3. All diodes are ideal. **Stage 1 [\(\mathbf{t_{0}}\), \(\mathbf{t_{1}}\)]:** Refer to Figure 2a for Stage 1. Switches \(SW_{1,wind}\) and \(SW_{2,wind}\) are closed, whereas \(SW_{1,pv}\) and \(SW_{1,pv}\) are opened. The wind-turbine input voltage \(V_{wind}\) forward energy to \(L_{m,wind}\) via the loop of \(V_{wind}\)-\(SW_{1,wind}\)-\(L_{k,wind}\)-\(L_{m,wind}\)-\(SW_{2,wind}\). Meanwhile, the output inductor \(L_{o}\) and capacitor \(C_{o}\) absorb energy from \(C_{2,wind}\), so that the current flowing through \(L_{o}\), \(i_{Lo}\), increases linearly. The capacitor \(C_{2,pv}\) is charged by the magnetizing inductor \(L_{m,pv}\). This stage ends as the \(SW_{1,wind}\) and \(SW_{2,wind}\) are turned off. **Stage 2 [\(\mathbf{t_{1}}\), \(\mathbf{t_{2}}\)]:** The equivalent of Stage is shown in Figure 2b. During this time interval, all the switches are open. The leakage inductor \(L_{k,wind}\) dumps energy to capacitor \(C_{wind}\) via the loop of \(L_{k,wind}\)-\(D_{1,wind}\)-\(C_{wind}\)-\(D_{2,wind}\). The current of the leakage inductor \(L_{k,wind}\), \(i_{lk,wind}\), decreases rapidly. At output, the \(L_{o}\) powers output and its current decreases accordingly. This stage ends when the current \(i_{lk,wind}\) falls to 0. Figure 2: \(Cont.\)  
Figure 2: _Cont._  
**Stage 3 [t2, t3]:** Figure 2c depicts the equivalent circuit of this stage, in which all the switches are open. Magnetizing inductors, \(L_{m,wind}\) and \(L_{m,pv}\), release their energy to \(C_{2,wind}\) and \(C_{2,PV}\), respectively. The capacitor \(C_{1,wind}\) charges \(C_{o}\) by the loop of \(C_{o}\)-\(D_{4,wind}\)-\(C_{1,wind}\)-\(D_{5,wind}\)-\(L_{o}\). The operation of the converter enters into the next stage when \(SW_{1,pv}\) and \(SW_{2,pv}\) are simultaneously turned off. **Stage 4 [t3, t4]:** This stage begins at \(t=t_{4}\). Figure 2d illustrates the equivalent. In Stage 4, both switches \(SW_{1,pv}\) and \(SW_{2,pv}\) are closed, whereas \(SW_{1,wind}\) and \(SW_{1,wind}\) are opened. The PV input voltage \(V_{pv}\) forwards energy to \(L_{m,pv}\) through the loop of \(V_{pv}\)-\(SW_{1,pv}\)-\(L_{k,pv}\)-\(L_{m,pv}\)-\(SW_{2,pv}\). The energy stored in the magnetizing inductor \(L_{m,wind}\) is released to the secondary of the coupled inductor \(T_{1}\) to charge \(C_{2,wind}\). The inductor \(L_{o}\) and capacitor \(C_{o}\) absorb energy from \(C_{2,pv}\); therefore, the current of \(L_{o}\), \(i_{Lo}\), increases linearly. As the \(SW_{1,pv}\) and \(SW_{2,pv}\) are turned off again, this stage ends. **Stage 5 [t4, t5]:** As referred to in Figure 2e, it can be found that all the switches are in an off state in Stage 5. The leakage inductor \(L_{k,pv}\) charges capacitor \(C_{pv}\) and its current drops steeply. In addition, output inductor \(L_{o}\) pumps energy to \(C_{o}\), which results in a linear decrease at current \(i_{Lo}\). At the moment that current \(i_{L,pv}\) drops to 0, Stage 6 begins. Figure 3: Conceptual key waveforms of the DIPWC. Figure 2: Equivalent circuits of the DIPWC: (**a**) Stage 1, (**b**) Stage 2, (**c**) Stage 3, (**d**) Stage 4, (**e**) Stage 5, and (**f**) Stage 6. **Stage 6 [\(t_{5}\), \(t_{6}\)]:** Figure 2f shows the equivalent circuit of this stage, in which all the switches are open.