# LLC Resonant Voltage Multiplier-Based Differential Power Processing Converter Using Voltage Divider with Reduced Voltage Stress for Series-Connected Photovoltaic Panels under Partial Shading

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## Abstract

**:**

## 1. Introduction

_{string}, flows through a bypass diode that is connected in parallel with a shaded panel, as illustrated in Figure 1a. The bypassed panel no longer generates power as its voltage is subzero value, significantly reducing the power generation of the string as a whole. An annual energy yield reportedly deteriorates by 20%–30% due to partial shading on a PV panel [1]. Furthermore, partial shading generates multiple maximum power points (MPPs), including one global and some local MPPs, on a P–V characteristic of the partially-shaded string that might hinder and confuse ordinary MPP tracking (MPPT) algorithms—the shaded PV panel might operate at a local MPP, at which the panel generates less power than at the global MPP, as shown in Figure 1b. Although advanced MPPT techniques have been proposed to certainly track the global MPP even under partial shading conditions [2], a shaded panel is bypassed and cannot contribute to power generation, unavoidably resulting in reduced energy yield.

_{string}of several hundred volts. Three-level converters based on a neutral-point diode-clamped converter [32] and an LLC resonant converter (see Figure 3) [33] have been proposed to mitigate voltage stress issues, and voltage stresses of switches and capacitors can be reduced to V

_{string}/2. However, these circuit components are still exposed to high voltage stresses in high-voltage PV strings.

## 2. Proposed DPP Converter Based on Voltage Divider and LLC Resonant Voltage Multiplier

#### 2.1. Key Circuits for Proposed DPP Converter

_{in}and C

_{out}, can be automatically balanced.

_{b}and Q

_{a}) are driven at a fixed frequency with a fixed 50% duty cycle in a complementary manner, and the LLC resonant tank is driven by a square-wave voltage with a peak-to-peak voltage of V

_{string}, as shown in the inset of Figure 4c. A sinusoidal current generated by the LLC resonant tank is transferred to the secondary side and is rectified by the VM. Eventually, the VM produces uniform multiple output voltages, by which PV substring characteristics are automatically unified even without feedback control [28,29,30,31].

#### 2.2. Proposed DPP Converter

_{1}–Q

_{4}and input smoothing capacitors C

_{in1}–C

_{in4}. Body diodes (D

_{Q1}–D

_{Q4}) and parasitic output capacitances (C

_{Q1}–C

_{Q4}) of MOSFETs, which play important roles to achieve zero voltage switching (ZVS) operations, are also illustrated. A leakage inductance L

_{r}and magnetizing inductance L

_{mg}of the transformer are utilized for the resonant operation. The VD comprises the SCC containing inductors, while the LLC resonant inverter is very similar to that in the conventional DPP converter shown in Figure 4c. For the sake of clarity, the circuit on the VD side is defined as a transformer’s primary side, and the secondary side is the VM. The string voltage V

_{string}is divided into four by the SCC and PWM converters in the VD, achieving the reduced voltage stresses of circuit components on the primary side.

_{in1}–C

_{in2}, C

_{in3}–C

_{in4}, and C

_{r1}–C

_{r2}) act as capacitors C

_{1}, C

_{2}, and C

_{3}in the traditional SCC (see Figure 4a), respectively. C

_{r1}and C

_{r2}also behave like resonant capacitors. Meanwhile, thanks to the added inductors of L

_{1}and L

_{2}, and the magnetizing inductor L

_{mg}of the transformer, three PWM converters can be formed in the VD. By driving switches with a fixed 50% duty cycle, all capacitor voltages are automatically balanced to be V

_{string}/4 by the SCC and PWM converters in the VD.

_{r1}and C

_{r2}, and L

_{mg}form an LLC resonant tank that produces ac current and voltage. The ac power generated by the LLC resonant tank is transferred to the secondary side, and the transferred power is automatically redistributed to shaded panels having weak characteristics. This power redistribution realizes automatic characteristic equalization. The detailed operation principle and mechanism of this power redistribution have been reported and discussed in detail in the past work [28].

#### 2.3. Major Features

_{string}/4 and V

_{string}/2, respectively. The circuit on the right-hand side corresponds to the case of n = 6, and voltage stresses of capacitors and switches can be reduced to V

_{string}/6 and V

_{string}/3, respectively. Either L

_{2}or L

_{4}, or both of them, is replaced with a magnetizing inductance of a transformer to form an LLC resonant VM. Similarly, by extending the circuit to n = 8, the voltage stresses of capacitors and switches can be further reduced to V

_{string}/8 and V

_{string}/4.

#### 2.4. Extended Topology of Proposed DPP Converter

_{1}for PV

_{1}–PV

_{4}, and VM

_{2}for PV

_{5}–PV

_{8}). V

_{string}is divided into six in the VD, allowing reduced voltage stresses of capacitors and switches, as mentioned in Section 2.3. L

_{2}and L

_{4}in the VD in Figure 6 are replaced with transformers’ magnetizing inductances, L

_{mg1}and L

_{mg2}, respectively. An operation mechanism of VMs in the extended topology is identical to that of the VM in Figure 5a. Hence, in the next section, the operation analysis is performed only for the basic topology for the sake of clarity.

## 3. Operation Analysis

#### 3.1. Operation Principle

_{1}only is partially shaded. Key operation waveforms and current flow paths are shown in Figure 8 and Figure 9, respectively. All switches are driven with a fixed duty cycle with a proper dead time period. Current and voltage waveforms of Q

_{1}and Q

_{2}are identical to those of Q

_{4}and Q

_{3}, and therefore, waveforms of Q

_{1}and Q

_{2}only are illustrated and discussed in this section. Capacitances of the resonant capacitors of C

_{r1}and C

_{r2}are assumed identical.

_{1}and Q

_{2}, v

_{DS1}and v

_{DS2}, are zero and V

_{string}/2, respectively. The series connection of C

_{in1}and C

_{in2}is connected in parallel with the series connection of C

_{r1}and C

_{r2}, and therefore, voltages of these series-connected capacitors become uniform. Currents of L

_{1}, L

_{2}, and L

_{mg}(i

_{L1}, i

_{L2}, and i

_{Lmg}) linearly increase as they are charged by C

_{in1}, C

_{in3}, and C

_{r2}, respectively. Meanwhile, the current of L

_{r}, i

_{Lr}, sinusoidally changes due to the resonance between L

_{r}and C

_{r1}–C

_{r2}. A current equal to i

_{Lr}– i

_{Lmg}is transferred to the secondary side in the form of i

_{VM}= N (i

_{Lr}− i

_{Lmg}) where N (= N

_{1}/N

_{2}) is the transformer turn ratio. C

_{1}in the VM is charged by i

_{VM}through the diode D

_{2}. After half the resonant period, i

_{Lr}becomes equal to i

_{Lmg}, and the operation shifts to the next mode.

_{Lmg}and i

_{Lr}are equal and linearly increase. In the VD, i

_{L1}and i

_{L2}still linearly increase. On the secondary side, no currents flow in the VM, except for output smoothing capacitors.

_{1}, v

_{GS1}is removed to turn off Q

_{1}, and C

_{Q1}and C

_{Q2}start to be charged and discharged by i

_{Lmg}, respectively. v

_{DS1}increases with a slope, thus achieving ZVS turn-off. Meanwhile, v

_{DS2}decreases with a slope equal to that of v

_{DS1}because the sum of v

_{DS1}and v

_{DS2}is always equal to the total voltage of C

_{in1}and C

_{in2}(i.e., V

_{string}/2). This turn-off operation is essentially identical to that of traditional LLC resonant converters.

_{Q1}and C

_{Q2}are completed. v

_{DS1}and v

_{DS2}become V

_{string}/2 and 0, respectively, and the body diode of Q

_{2}, D

_{Q2}, starts conducting. Meanwhile, i

_{L1}, i

_{L2}, and i

_{Lmg}start linearly decreasing as they are charged by C

_{in2}, C

_{in4}, and C

_{r1}, respectively. Sinusoidal resonant current i

_{Lr}starts flowing again due to the resonance between L

_{r}and C

_{r1}–C

_{r2}. In the VM, i

_{VM}flows through the low-side diode, D

_{1}.

_{Q2}is conducting (i.e., v

_{DS2}= 0), the gating signal for Q

_{2}, v

_{GS2}, is applied to turn on Q

_{2}to achieve ZVS turn-on. This operation mode is symmetric to Mode 1.

_{L1}and i

_{L2}are zero, small inductors with a small current rating can be used for L

_{1}and L

_{2}. In the VM, currents flow through diodes and a capacitor that are connected to the shaded panel of PV

_{1}, while other diodes and capacitors are not in operation. Average current of a capacitor under steady-state conditions must be zero, and therefore, an equalization current supplied from the DPP converter to PV

_{1}is equal to an average current of D

_{1}or D

_{2}.

#### 3.2. Operation Boundary

_{s}, f

_{r}, and f

_{0}are the switching frequency, higher resonant frequency, and lower resonant frequency, respectively.

#### 3.3. Voltage Equalization Mechanism of Voltage Multiplier

_{VM}with a peak-to-peak value of V

_{pp}into a dc voltage with a magnitude of V

_{pp}. In Figure 10, for example, when an ac voltage v

_{VM}with V

_{pp}= V

_{PV}is inputted, the VM produces uniform output voltages of V

_{PV}across C

_{out1}–C

_{out4}. C

_{1}–C

_{4}in the VM behave as ac coupling capacitors that block dc currents and allow ac components only to flow through them. Hence, by removing dc components, the VM can be transformed to an equivalent circuit shown on the right-hand side, in which all the PV panels are separated and grounded. Since all PV panels are equivalently connected in parallel, all the voltages of panels as well as C

_{out1}–C

_{out4}are automatically equalized. Detailed operation analyses have been performed in past works [28].

#### 3.4. Design Guideline for LLC Resonant Inverter

_{mg}to L

_{r}for ordinary LLC resonant converters is designed to be around 5–10 in order to obtain proper gain-frequency characteristics [34]; ratios vary depending on applications but do not exceed 10 in most applications. The proposed LLC resonant VM-based DPP converter, on the other hand, operates at a fixed switching frequency with a fixed duty cycle. Since ordinary PV panels are generally installed so that partial shading does not occur as far as possible, the proposed DPP converter should be designed to minimize the loss under unshaded conditions, which correspond to no-load conditions for ordinary LLC resonant converters. A small value in L

_{mg}leads to an increased loss due to a large i

_{Lmg}under no-load conditions. Hence, to reduce the loss originating from i

_{Lmg}, L

_{mg}in the proposed DPP converter should be designed to be large within the range that i

_{Lmg}can completely charge and discharge C

_{Q}of MOSFETs in order to achieve the ZVS operations.

_{r}to L

_{mg}of the LLC resonant tank (approximately 150 in the prototype, see Table 1) is rather larger than that of ordinary LLC resonant converter (around 5–10), the LLC resonant tank in the proposed DPP converter operates more like a series-resonant tank. Therefore, similar to traditional series-resonant tanks, the gain of the LLC resonant tank in the proposed DPP converter is unity at the higher resonant frequency f

_{r}. It suggests the turns ratio of the transformer can be determined by assuming the unity gain of the LLC resonant tank.

_{1}and C

_{r2}are alternately applied to the transformer primary winding, and V

_{pp}is equal to V

_{string}/2. As mentioned in Section 3.3, the voltages of the VM’s outputs (i.e., C

_{out1}–C

_{out4}) are equal to the peak-to-peak value of the VM’s input voltage v

_{VM}(or the voltage of the secondary winding), yielding the following equation:

_{PV}is the voltage of the panel that receives an equalization current from the DPP converter. Assuming all voltages are ideally equalized to be V

_{PV}, substituting V

_{string}= 4V

_{PV}into (2) produces:

_{2}is slightly larger than N

_{1}(i.e., 2N

_{2}> N

_{1}).

#### 3.5. Peak Current of Inductor

_{string}is divided by the VD, the voltages applied to the inductors in the VD can be reduced, contributing to reduced peak inductor currents. The peak current of the inductors, I

_{L.peak}, can be yielded as:

_{Cin}is the voltage of C

_{in1}–C

_{in4}, T

_{s}(= 1/f

_{s}) is the switching period, and L is the inductance. Applying the experimental conditions (V

_{string}= 142.5 V, V

_{Cin}= 35.6 V, T

_{s}= 7.15 μs, and L = 470 μH), I

_{L.peak}is calculated to be 136 mA. Although V

_{string}is 142.5 V, I

_{L.peak}can be as low as 136 mA with L = 470 μH thanks to the zero average currents of the inductors.

## 4. Experimental Results

#### 4.1. Prototype

_{r1}and C

_{r2}, MLCCs were employed as capacitors in the prototype. The higher resonant frequency f

_{r}was 164 kHz, and the prototype was operated at f

_{s}= 140 kHz with a dead time period of 0.4 μs.

#### 4.2. Fundamental Characteristics of DPP Converter

_{in}. A variable resistor R

_{var}was connected to the output of the VM through the selective tap to emulate current flow paths under partial shading conditions. Selecting tap X, for example, can emulate the current flow paths under the case that PV

_{1}is partially shaded. With the tap Y selected, the prototype behaves as if PV

_{1}and PV

_{2}are uniformly shaded. V

_{in}was set to be 142.5 V, which corresponded to an MPP voltage of the string used for the experiment.

_{Rvar}= 1.5 A with the tap X selected are shown in Figure 13. Peak voltages of v

_{DS1}and v

_{DS2}were about 71.3 V, nearly half the input voltage V

_{in}of 142.5 V, demonstrating that the input voltage was properly divided by the VD. Measured waveforms of v

_{GS1}, v

_{GS2}, v

_{DS1}, and v

_{DS2}were in good agreement with theoretical ones (see Figure 8), demonstrating ZVS turn-on and turn-off operations.

_{Cout1}on the horizontal axis corresponds to the voltage of C

_{out1}or the voltage of the shaded panel in the practical case. Voltages of C

_{out1}–C

_{out4}were nearly uniform thanks to the voltage equalization performance of the VM. The measured efficiencies were mostly higher than 90%. V

_{Cout1}linearly declined as I

_{Rvar}increased, and this tendency was more explicit when the tap Y was selected. It was because, with the tap Y selected, the input current of the prototype was twice that with the tap X selected, causing larger voltage drops in the VD on the transformer primary side.

#### 4.3. Equalization Test in Laboratory

_{3}was a partially shaded panel, and its short-circuit current was 30% less than the others. The ideal maximum power of the string under this partial shading condition was 623 W. An electronic load was connected to the load port (see the port denoted as Load+ and Load− in Figure 5a) in order to sweep the string characteristics. A string characteristic without the DPP converter (i.e., with traditional bypass diodes) was also measured as a reference.

_{string}= 108 V. With the DPP converter, on the other hand, the local MPP disappeared, and the maximum power increased to as high as 617 W at V

_{string}= 143 V, corresponding to 21.9%. The overall efficiency, which is defined as the ratio of the extracted power to the ideal maximum power, was determined to be 99.0% (= 617/623). The proposed DPP converter successfully increased the energy yield and demonstrated its efficacy.

_{3}for equalization. Due to the support by the DPP converter, the string behaved as if it produced 670 W. However, since 53 W out of 670 W was inputted to the DPP converter, the extracted power at the load port was 617 W. The power processed by the DPP converter under this partial shading condition was merely 53 W and was rather smaller than the string power. This small processed power allowed the 99% overall efficiency, even though the measured efficiency of the DPP converter was around 90% (see Figure 14).

#### 4.4. Field Testing

_{3}was covered with a plastic bag to emulate the partial shading condition. Measured individual panel characteristics are shown in Figure 18a. The irradiance was measured to be 591 W/m

^{2}by a pyranometer (ES-602, EKO). The short-circuit current of PV

_{3}was 16.7% less than the others. The ideal maximum power under this shading condition was 672 W. Similar to the laboratory testing, string characteristics with/without the DPP converter were swept using the electronic load.

_{string}= 130 V. With the DPP converter, the local MPP vanished, and the maximum power increased to 652 W at V

_{string}= 121 V, corresponding to the overall efficiency of 97.0% (= 652/672). These results demonstrate the improved energy yield of the actual PV string.

#### 4.5. Extended DPP Converter for Eight Panels Connected in Series

_{3}and PV

_{7}were shaded panels, and their short-circuit current was 15% less than the others. The ideal maximum power of the string was 1294 W.

_{string}= 292 V. With the DPP converter, on the other hand, the local MPP vanished, and the maximum power increased to 1289 W at V

_{string}= 288 V, corresponding to 8.2% improvement. The overall efficiency was as high as 99.6% (=1289/1294). The results demonstrated the extension concept of the proposed DPP converter.

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

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**Figure 1.**Characteristics under partial shading conditions: (

**a**) Current path and panel characteristics; (

**b**) String characteristics.

**Figure 2.**Differential power processing (DPP) architectures: (

**a**) Adjacent panel-to-panel architecture; (

**b**) Panel-to-panel with isolated port architecture; (

**c**) String-to-panel architecture.

**Figure 4.**Key circuits for proposed DPP converter: (

**a**) Switched capacitor converter (SCC); (

**b**) Bidirectional PWM converter; (

**c**) LLC resonant voltage multiplier (VM).

**Figure 5.**(

**a**) Proposed DPP converter based on voltage divider (VD) and LLC resonant voltage multiplier (VM); (

**b**) Voltage divider.

**Figure 11.**Prototype capable of supplying 60 W for each shaded panel in PV string consisting of four panels connected in series.

**Figure 15.**Experimental results of laboratory testing. (

**a**) Individual panel characteristics used for experiment; (

**b**) Measured string characteristics with/without proposed DPP converter.

**Figure 18.**Experimental results of field testing. (

**a**) Individual panel characteristics used for experiment; (

**b**) Measured string characteristics with/without proposed DPP converter.

**Figure 19.**Experimental results of extended DPP converter. (

**a**) Individual panel characteristics used for experiment; (

**b**) Measured string characteristics with/without proposed DPP converter.

Component | Value |
---|---|

Q_{1}–Q_{4} | IRF644PSBF, V_{DS} = 250 V, R_{on} = 0.28 Ω, C_{Q} = 330 pF |

C_{in1}–C_{in4} | MLCC, 40 μF (= 10 μF × 4), 100 V |

C_{r1}, C_{r2} | Film Capacitor, 400 nF (= 100 nF × 4), 100 V |

L_{1}, L_{2} | 470 μH |

C_{1}–C_{4} | MLCC, 20 μF (= 10 μF × 2), 100 V |

C_{out1}–C_{out4} | MLCC, 50 μF (= 10 μF × 5), 50 V |

D_{1}–D_{8} | Schottky Diode, SBRT20M60SP5, V_{D} = 0.57 V |

Transformer | N_{1}:N_{2} = 13:7, L_{r} = 1.18 μH, L_{mg} = 175 μH, R_{Tp} = 1.77 Ω, R_{Ts} = 1.77 Ω |

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**MDPI and ACS Style**

Uno, M.; Nakane, T.; Shinohara, T.
LLC Resonant Voltage Multiplier-Based Differential Power Processing Converter Using Voltage Divider with Reduced Voltage Stress for Series-Connected Photovoltaic Panels under Partial Shading. *Electronics* **2019**, *8*, 1193.
https://doi.org/10.3390/electronics8101193

**AMA Style**

Uno M, Nakane T, Shinohara T.
LLC Resonant Voltage Multiplier-Based Differential Power Processing Converter Using Voltage Divider with Reduced Voltage Stress for Series-Connected Photovoltaic Panels under Partial Shading. *Electronics*. 2019; 8(10):1193.
https://doi.org/10.3390/electronics8101193

**Chicago/Turabian Style**

Uno, Masatoshi, Toru Nakane, and Toshiki Shinohara.
2019. "LLC Resonant Voltage Multiplier-Based Differential Power Processing Converter Using Voltage Divider with Reduced Voltage Stress for Series-Connected Photovoltaic Panels under Partial Shading" *Electronics* 8, no. 10: 1193.
https://doi.org/10.3390/electronics8101193