3. Operation analysis

will be discussed in Section 4. The experimental results of the laboratory and field testing for a

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

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

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

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

standard 72-cell PV panel consisting of three substrings will be presented in Section 5.

2. Proposed single-switch DPP converter

equalization mechanisms can be found elsewhere [12, 14].

are virtually unified even under partial shading conditions.

by adding diodes and capacitors in the VM, allowing a flexible design.

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

2.1. Key elements for proposed DPP converter

discussed in Section 3.

134 Solar Panels and Photovoltaic Materials

#### 3.1. Automatic voltage equalization mechanism

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

capacitors can be regarded as AC-coupling capacitors that allow AC components only to flow through them. Hence, substrings as well as parallel-connected voltage doublers, each comprising diode pairs and a coupling capacitor, can be equivalently separated and grounded, as shown in Figure 6. All the substrings with respective voltage doublers in this equivalent circuit are connected in parallel, and therefore, AC current preferentially flows through a voltage doubler that is connected to a shaded substring whose voltage tends to be lower than the others.

#### 3.2. Operation principle

This section discusses the operation analysis in the case that PV1 is partially shaded. The proposed DPP converter operates either in continuous conduction mode (CCM) or discontinuous conduction mode (DCM). The DCM operation, which contains more operation modes, is discussed in this section. Key operation waveforms and current flow directions are shown in Figures 7 and 8, respectively. The lossless snubber is depicted as a voltage source Vsn with a diode Dsn, in Figure 8, for the sake of clarity.

The average voltage of Cr is zero thanks to Rbias and the transformer secondary winding whose average voltage must be zero under steady-state conditions. Hence, the input voltage of the VM, vVM, is nearly identical to the voltage of secondary winding, vS.

Mode 1 (T0–T1) (Figure 8(a)): The switch Q is turned on, and the DPP converter operates in the forward mode. The current of Lmg, iLmg, starts linearly increasing from zero, as

$$i\_{Lmg} = \frac{V\_{string}}{L\_{mg} + L\_{kg}}(t - T\_0) \tag{1}$$

Meanwhile, Lkg resonates with Cr on the secondary winding, and sinusoidal current iCr flows;

Single-Switch Differential Power Processing PWM Converter to Enhance Energy Yield of Photovoltaic Panels…

where Zr and ω<sup>r</sup> are the characteristic impedance of the resonant tank and resonant angular

The current of Lkg, iLkg, is equal to the sum of iLmg and iCr reflected on the primary side. In the VM, the upper diode corresponding to PV1, D2, conducts whereas other diodes are off. Since the voltage of Cr can be approximated to be zero, vVM during the even-numbered diodes are

, <sup>ω</sup><sup>r</sup> <sup>¼</sup> <sup>2</sup>π<sup>f</sup> <sup>r</sup> <sup>¼</sup> <sup>N</sup>

ffiffiffiffiffiffiffiffiffiffiffi LkgCr

Zr j j sin <sup>ω</sup>rð Þ <sup>t</sup> � <sup>T</sup><sup>0</sup> (2)

<sup>p</sup> (3)

http://dx.doi.org/10.5772/intechopen.74307

137

<sup>N</sup> � VVM:<sup>O</sup>

ffiffiffiffiffiffi Lkg Cr

s

iCr ¼

Figure 7. Key operation waveforms when PV1 is partially shaded.

Zr ¼ N

frequency given by

on, VVM.E, is given by

Vstring

Figure 6. Equivalent circuit of voltage multiplier.

Single-Switch Differential Power Processing PWM Converter to Enhance Energy Yield of Photovoltaic Panels… http://dx.doi.org/10.5772/intechopen.74307 137

Figure 7. Key operation waveforms when PV1 is partially shaded.

capacitors can be regarded as AC-coupling capacitors that allow AC components only to flow through them. Hence, substrings as well as parallel-connected voltage doublers, each comprising diode pairs and a coupling capacitor, can be equivalently separated and grounded, as shown in Figure 6. All the substrings with respective voltage doublers in this equivalent circuit are connected in parallel, and therefore, AC current preferentially flows through a voltage doubler

This section discusses the operation analysis in the case that PV1 is partially shaded. The proposed DPP converter operates either in continuous conduction mode (CCM) or discontinuous conduction mode (DCM). The DCM operation, which contains more operation modes, is discussed in this section. Key operation waveforms and current flow directions are shown in Figures 7 and 8, respectively. The lossless snubber is depicted as a voltage source Vsn with a

The average voltage of Cr is zero thanks to Rbias and the transformer secondary winding whose average voltage must be zero under steady-state conditions. Hence, the input voltage of the

Mode 1 (T0–T1) (Figure 8(a)): The switch Q is turned on, and the DPP converter operates in the

Lmg þ Lkg

ð Þ t � T<sup>0</sup> (1)

that is connected to a shaded substring whose voltage tends to be lower than the others.

3.2. Operation principle

136 Solar Panels and Photovoltaic Materials

diode Dsn, in Figure 8, for the sake of clarity.

Figure 6. Equivalent circuit of voltage multiplier.

VM, vVM, is nearly identical to the voltage of secondary winding, vS.

forward mode. The current of Lmg, iLmg, starts linearly increasing from zero, as

iLmg <sup>¼</sup> Vstring

Meanwhile, Lkg resonates with Cr on the secondary winding, and sinusoidal current iCr flows;

$$i\_{\rm Gr} = \frac{\frac{V\_{\rm string}}{N} - V\_{VMO}}{|Z\_r|} \sin \omega\_r (t - T\_0) \tag{2}$$

where Zr and ω<sup>r</sup> are the characteristic impedance of the resonant tank and resonant angular frequency given by

$$Z\_r = N \sqrt{\frac{L\_{\text{kg}}}{\mathcal{C}\_r}} \,\omega\_r = 2\pi f\_r = \frac{N}{\sqrt{L\_{\text{kg}}\mathcal{C}\_r}} \tag{3}$$

The current of Lkg, iLkg, is equal to the sum of iLmg and iCr reflected on the primary side. In the VM, the upper diode corresponding to PV1, D2, conducts whereas other diodes are off. Since the voltage of Cr can be approximated to be zero, vVM during the even-numbered diodes are on, VVM.E, is given by

$$V\_{VME} = V\_{C1} + V\_f = \frac{L\_{\text{mg}}V\_{\text{string}}}{N\left(L\_{\text{kg}} + L\_{\text{mg}}\right)}\tag{4}$$

As iCr reaches zero, this mode ends, and the operation moves to the next mode.

Mode 2 (T1–T2) (Figure 8(b)): Q is still on, but all resonant currents become zero. Since iCr is zero, iLkg is identical to iLmg. No current flows in the VM, except for the current from the smoothing capacitor Cout1 to PV1. In order for Mode 2 to exist, Mode 1 must be longer than half the resonant period. Hence, the following equation needs to be satisfied;

$$d \ge \frac{f\_S}{2f\_r} \tag{5}$$

iLmg begins to decrease as Lmg starts releasing its energy stored in the first two modes. iLmg is transferred to the secondary side, and the lower diode corresponding to PV1, D1, conducts. This mode ends as iLkg becomes zero—the length of this mode is practically very short compared to

Single-Switch Differential Power Processing PWM Converter to Enhance Energy Yield of Photovoltaic Panels…

Mode 4 (T3–T4) (Figure 8(d)): iLmg keeps decreasing, and its energy is released to the secondary

VVM:<sup>O</sup> <sup>¼</sup> VPV<sup>1</sup> <sup>þ</sup> Vf � VC<sup>1</sup> <sup>¼</sup> VPV<sup>1</sup> <sup>þ</sup> <sup>2</sup>Vf � LmgVstringmg

If the operation meets d' < (1 � d), the DPP converter operates in DCM. The critical duty cycle

Mode 5 (T4–T5) (not shown): This mode is unique to the DCM operation. No currents flow in

In summary, the upper and lower diodes that are connected in parallel with the shaded substring alternately conduct. The shaded substring PV1 receives the current from the DPP

Since the average voltage of Cr is nearly zero, vVM can be assumed equal to vS. Based on voltsecond balance on the transformer secondary winding with Eqs. (4) and (8), the voltage

VPV<sup>1</sup> <sup>¼</sup> LmgVstring <sup>d</sup> <sup>þ</sup> <sup>d</sup><sup>0</sup> ð Þ

The voltage conversion ratio in CCM can be obtained by applying d' = 1 – d into (11), as

Eqs. (11) and (12) suggest that the voltage conversion ratio is PWM-controllable, and d should be properly adjusted depending on the degree of shading. The control strategy suitable for the

VPV<sup>1</sup> <sup>¼</sup> LmgVstring

N Lmg <sup>þ</sup> Lkg VPV1 <sup>þ</sup> <sup>2</sup>Vf

Lmg

Lmg � Vstring

ð Þ t � T<sup>3</sup> (7)

http://dx.doi.org/10.5772/intechopen.74307

(10)

Nd<sup>0</sup> Lkg <sup>þ</sup> Lmg � <sup>2</sup>Vf (11)

<sup>N</sup>ð Þ <sup>1</sup> � <sup>d</sup> Lkg <sup>þ</sup> Lmg � <sup>2</sup>Vf (12)

N Lkg <sup>þ</sup> Lmg (8)

(9)

139

iLmg <sup>¼</sup> ILmg:peak � NVVM:<sup>E</sup>

<sup>d</sup><sup>0</sup> <sup>¼</sup> dVstring N VPV1 þ 2Vf LmgþLkg

dcritical <sup>&</sup>lt; <sup>1</sup> � VstringLmg

the DPP converter, except for Cout1 providing a current to the shaded substring PV1.

converter, whereas no current flows toward unshaded substrings.

proposed DPP PWM converter is discussed in the next section.

conversion ratio of the proposed DPP converter in DCM can be yielded as

vVM during odd-numbered diodes are on, VVM.O, is expressed using (4) as

other modes.

side. iLmg in this mode is expressed as

The duty cycle of Mode 4, d' = (T3–T4)/TS, is

for DCM operation, dcritical, is given by

where d is the duty cycle of Q. The peak value of iLmg at the end of this mode, ILmg.peak is

$$I\_{L\text{mg,peak}} = \frac{V\_{string}dT\_S}{L\_{\text{mg}} + L\_{\text{kg}}} \tag{6}$$

Mode 3 (T2–T3) (Figure 8(c)): Q is turned off, and the DPP converter starts operating in the flyback mode. The energy stored in Lkg in Modes 1 and 2 is absorbed by the snubber. Meanwhile,

Figure 8. Current flow directions in (a) mode 1, (b) mode 2, (c) mode 3, and (d) mode 4.

iLmg begins to decrease as Lmg starts releasing its energy stored in the first two modes. iLmg is transferred to the secondary side, and the lower diode corresponding to PV1, D1, conducts. This mode ends as iLkg becomes zero—the length of this mode is practically very short compared to other modes.

Mode 4 (T3–T4) (Figure 8(d)): iLmg keeps decreasing, and its energy is released to the secondary side. iLmg in this mode is expressed as

$$\dot{\mathbf{i}}\_{L\text{mg}} = I\_{L\text{mg},\text{peak}} - \frac{NV\_{V\text{ME}}}{L\_{\text{mg}}}(t - T\_3) \tag{7}$$

vVM during odd-numbered diodes are on, VVM.O, is expressed using (4) as

$$V\_{VMO} = V\_{PV1} + V\_f - V\_{C1} = V\_{PV1} + 2V\_f - \frac{L\_{\rm mg} V\_{\rm string\,mg}}{N\left(L\_{\rm kg} + L\_{\rm mg}\right)}\tag{8}$$

The duty cycle of Mode 4, d' = (T3–T4)/TS, is

VVM:<sup>E</sup> <sup>¼</sup> VC<sup>1</sup> <sup>þ</sup> Vf <sup>¼</sup> LmgVstring

Mode 2 (T1–T2) (Figure 8(b)): Q is still on, but all resonant currents become zero. Since iCr is zero, iLkg is identical to iLmg. No current flows in the VM, except for the current from the smoothing capacitor Cout1 to PV1. In order for Mode 2 to exist, Mode 1 must be longer than

> <sup>d</sup> <sup>≥</sup> <sup>f</sup> <sup>S</sup> 2f r

ILmg:peak <sup>¼</sup> VstringdTS

Mode 3 (T2–T3) (Figure 8(c)): Q is turned off, and the DPP converter starts operating in the flyback mode. The energy stored in Lkg in Modes 1 and 2 is absorbed by the snubber. Meanwhile,

Lmg þ Lkg

where d is the duty cycle of Q. The peak value of iLmg at the end of this mode, ILmg.peak is

As iCr reaches zero, this mode ends, and the operation moves to the next mode.

138 Solar Panels and Photovoltaic Materials

half the resonant period. Hence, the following equation needs to be satisfied;

Figure 8. Current flow directions in (a) mode 1, (b) mode 2, (c) mode 3, and (d) mode 4.

N Lkg þ Lmg

(4)

(5)

(6)

$$d' = \frac{dV\_{\rm string}}{N(V\_{PV1} + 2V\_f)\frac{L\_{\rm gy} + L\_{\rm gy}}{L\_{\rm my}} - V\_{\rm string}}\tag{9}$$

If the operation meets d' < (1 � d), the DPP converter operates in DCM. The critical duty cycle for DCM operation, dcritical, is given by

$$d\_{critical} < 1 - \frac{V\_{string}L\_{mg}}{N\left(L\_{mg} + L\_{kg}\right)\left(V\_{PV1} + 2V\_f\right)}\tag{10}$$

Mode 5 (T4–T5) (not shown): This mode is unique to the DCM operation. No currents flow in the DPP converter, except for Cout1 providing a current to the shaded substring PV1.

In summary, the upper and lower diodes that are connected in parallel with the shaded substring alternately conduct. The shaded substring PV1 receives the current from the DPP converter, whereas no current flows toward unshaded substrings.

Since the average voltage of Cr is nearly zero, vVM can be assumed equal to vS. Based on voltsecond balance on the transformer secondary winding with Eqs. (4) and (8), the voltage conversion ratio of the proposed DPP converter in DCM can be yielded as

$$V\_{PV1} = \frac{L\_{\rm mg} V\_{\rm string} (d + d')}{\rm Nd'(L\_{\rm kg} + L\_{\rm mg})} - 2V\_f \tag{11}$$

The voltage conversion ratio in CCM can be obtained by applying d' = 1 – d into (11), as

$$V\_{PV1} = \frac{L\_{\rm mg} V\_{\rm string}}{N(1 - d) \left(L\_{\rm kg} + L\_{\rm mg}\right)} - 2V\_f \tag{12}$$

Eqs. (11) and (12) suggest that the voltage conversion ratio is PWM-controllable, and d should be properly adjusted depending on the degree of shading. The control strategy suitable for the proposed DPP PWM converter is discussed in the next section.
