2. Proposed single-switch DPP converter

#### 2.1. Key elements for proposed DPP converter

The proposed string-to-substring DPP converter is essentially the combination of the FFRI and VM, shown in Figure 4(a) and (b), respectively. As the switch Q is turned on, the FFRI operates in the forward mode, in which the leakage inductance of the transformer, Lkg, resonates with the resonant capacitor Cr placed on the secondary side. At the same time, the magnetizing inductance Lmg stores energy. As Q is turned off, the FFRI operates in the flyback mode, and the stored energy in Lmg is released to the secondary side. The energy stored in Lkg is absorbed in a snubber circuit in order to prevent a voltage spike applied to Q. In summary, AC voltage/ current is generated across the secondary winding. The detailed operation analysis will be discussed in Section 3.

The VM basically comprises multiple voltage doublers stacked in series—three voltage doublers, each consisting of a coupling capacitor, diode pair, and a smoothing capacitor, are stacked in Figure 4(b). The VM is driven by AC current/voltage produced by the FFRI. The upper and lower diodes (i.e., the even- and odd-numbered diodes) alternately conduct as AC current/voltage is applied. Voltages of smoothing capacitors Cout1–Cout3 are automatically unified without feedback control, and therefore, voltages of PV substrings that are connected in parallel with respective smoothing capacitors are automatically equalized. Detailed voltage equalization mechanisms can be found elsewhere [12, 14].

### 2.2. Circuit description of single-switch DPP converter and its features

The proposed single-switch DPP converter for three substrings is shown in Figure 5. The output of the FFRI is connected to the input of the VM, and therefore, the VM is driven by AC voltage/current produced by the FFRI [15]. A bias resistor Rbias is added to stabilize voltages of the resonant capacitor Cr and coupling capacitors C1–C3; Cr and coupling capacitors C1–C3 are connected in series, and therefore, their voltages become unstable if without a bias resistor. Although a lossless LCD snubber is employed in Figure 5, any snubber circuits, including traditional lossy RCD snubbers, can be used to protect the switch Q. The input of the FFRI is tied to the string, whereas the outputs (i.e., Cout1–Cout3) of the VM are connected in parallel with respective substrings. Therefore, a fraction of the string power is redistributed to shaded substrings through the proposed DPP converter so that all the substring characteristics are virtually unified even under partial shading conditions.

3. Operation analysis

(b) voltage multiplier (VM).

3.1. Automatic voltage equalization mechanism

Figure 4. Proposed single-switch DPP PWM converter based on FFRI and VM.

As mentioned in Section 2.2, the voltages of substrings are automatically nearly unified with the VM in the proposed DPP converter. The VM is driven by AC voltage/current generated by the FFRI, as illustrated in Figure 4(b). Since capacitors C1–C3 are connected to the AC terminal, these

Figure 5. Key elements for proposed single-switch DPP PWM converter: (a) forward-flyback resonant inverter (FFRI) and

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In addition to the single-switch topology, the magnetic component count is also only one, realizing not only simplified circuit but also miniaturized circuit design. Although the circuit shown in Figure 5 is for three substrings, the number of substrings can be arbitrarily extended by adding diodes and capacitors in the VM, allowing a flexible design.

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Figure 4. Proposed single-switch DPP PWM converter based on FFRI and VM.

Figure 5. Key elements for proposed single-switch DPP PWM converter: (a) forward-flyback resonant inverter (FFRI) and (b) voltage multiplier (VM).
