# A Multistage DC-DC Step-Up Self-Balanced and Magnetic Component-Free Converter for Photovoltaic Applications: Hardware Implementation

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## Abstract

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## 1. Introduction

_{DS-ON}, as voltage stress raised across the switch is equal to the output voltage [39,40,41]. Multilevel converters provide a suitable solution for power conversion because of the low voltage stress across each device [42]. High voltage is achieved by multilevel DC-DC converters using capacitors and diode circuitry at the output end and the output voltage level can be increased without actually disturbing the actual circuit. By varying the number of output levels and duty cycle, the voltage gain of multilevel converters can be varied [43,44]. For conventional multilevel converters, designing magnetic components like inductors is a complex task, which also induces electromagnetic emission noise. Other than these issues the presence of inductors and transformers in the power circuit degrades the integration capability and increases the cost, weight and size of the converters. Switched Capacitor (SC) power circuits provide good integration ability due to their small volume and weight, since magnetic components like transformers and inductors is not needed to design a SC converter [33].

_{max}) of a solar PV device. The Maximum Power Point Tracker can be used to adjust its input voltage to utilize the maximum photovoltaic output power and then transform this power to supply the varying voltage requirements. When the PV voltage is increased the current will ultimately decrease, and when the PV current is increased the voltage will ultimately decrease. Depending on parameters like irradiance and temperature the MPP of the I-V curve of a PV module changes dynamically. Therefore, the MPP needs to be located by a tracking algorithm as it is not known beforehand.

_{L}to the best possible output resistance of the PV module R

_{PV}(R

_{mpp}= V

_{mpp}/I

_{mpp}). Characteristic power-voltage and current-voltage graphs or curves are shown in Figure 6a.

_{PV}) is equal to the short circuit current (I

_{SC}) or the photovoltaic voltage (V

_{PV}) is equal to the open circuit voltage (V

_{OC}). Thus, it is possible to track the maximum power point (MPP) of a photovoltaic cell by regulating the operating voltage of V

_{PV}. In [45] Maximum Power Point Tracking is discussed for a reconfigurable switched-capacitor converter and in [46] a perturbation and observation (P&O) algorithm is discussed for DC-DC converters connected to photovoltaic generators. The concept to control power of a multistage magnetic component-free DC-DC converter is explained in Figure 6b–f. Thus, to regulate the operating voltage V

_{PV}, the ON time of the capacitor and number of stages (if the structure is reconfigurable) are two controlled parameters in the proposed system, therefore it forces the MPPT charge controller to extract the maximum power PV module to operate at a voltage close to the maximum power point which causes it to draw the maximum available power from the PV module.

## 2. Recent Transformer-Less and Inductor-Less DC-DC Converters

#### 2.1. Series-Parallel Switched Capacitor (SC) Converter

- Difficult to change the switching state of the converter due to the several switching elements.
- Unequal voltage across switches, thus power switches of various ratings are required.
- Series-parallel SC is bidirectional, but it is not possible to control the power flow. It depends on the voltages at the input and output DC buses.
- If switching is not properly controlled, it may instigate a charge unbalance situation among the converter capacitors.
- Non-modularity, since a large number of switches, gate drivers and diodes are required and the number of devices increases with the number of levels. Due to this a series parallel converter is large in size and has high cost.

#### 2.2. Flying Capacitor Multilevel DC-DC Converter (FCMDC)

- A large number of transistors and capacitors is required (2N the number of switches and N number of capacitors are required to design an N-level FCMDC), hence this converter is large in size and also has a high cost.
- Difficult to extend the power circuit to increase the number of stages to change the output conversion ratio since the converter does not have a modular structure.
- A complicated switching scheme is required to operate the converter.
- FCMDC is inefficient at high switching frequency when the ON time is comparable to the rise and fall time of the switches since; to transfer energy from the input source to the capacitors a very small time frame is allowed.
- Utilization of components is less. It is not possible to control the power circuit if any of the switches fails.

#### 2.3. Magnetic-Less Multilevel DC-DC Converter (MMDC)

_{in}and also it is independent of the duty cycle and conversion ratio of the converter. However, the following are the drawbacks of the MMDC:

- A very large number of switching devices and capacitors are required to design an MMDC N (N + 1) switches, N (N + 1) diodes and 0.5N (N + 1) capacitors are required to design the N-Level MMDCC.
- It is difficult to manage direction of power flow of the converter due to the greater number of transistors present in the conducting path.
- The power flow of the converter is also depends on the voltages at the input and output DC buses, thus it is not a good option for the applications where the source voltage may vary.

#### 2.4. Fibonacci DC-DC Converter

- A large number of control switches are required to design the converter (3N + 1 number of control switches are required to design an N-stage converter)
- The Fibonacci DC-DC converter follows the Fibonacci series and thus it is not possible to achieve voltage conversion ratios like 2, 4… (which are not present in the Fibonacci converter)
- It is not capable of transferring power in both directions.

#### 2.5. Modified Step-Up DC-DC Converter (Switch Mode DC-DC Converter)

- A large number of switching devices is required.
- It introduces high switching losses and thus the efficiency of the converter is less.
- Moreover, there is no extension of the circuit to increase the voltage conversion ratio.
- This converter is not suitable for high power high voltage applications due to the lower voltage conversion ratio.

#### 2.6. Switched Capacitor DC-DC Converter

#### 2.7. Multilevel Modular Capacitor Clamped DC-DC Converter (MMCCC)

- Using this topology a high voltage conversion ratio is achieved, but it requires a large number of switching devices and capacitors.
- The voltage stress across switches of the converter is high. For an N level MMCCC the voltage stress of N-2 switching devices is equal to 2V
_{in}and the remaining switches have V_{in}voltage stress.

## 3. Proposed Self-Balanced and Magnetic Component-Free Multistage DC-DC Converter

#### 3.1. Mode of Operation

_{b}and S

_{a}act as a short circuit (turned ON) and open circuit (turned OFF) respectively, and Mode 2 when switch S

_{a}and S

_{b}act as a short circuit (turned ON) and open circuit (turned OFF), respectively. Hence, switch S

_{a}and switch S

_{b}are complementary in operation. The proposed topology has simple control and is operated at a fixed duty cycle of 0.5 to provide voltage to photovoltaic devices. A complex gate driver is also not required to drive the switch; instead an oscillator is sufficient to provide a gated signal.

_{b}is turned ON and switch S

_{a}is turned OFF, capacitor C

_{12}is charged by input voltage through diode D

_{11}and switch S

_{b}when the voltage across capacitor C

_{12}is smaller than the input voltage. When the voltage across capacitors C

_{12}+ C

_{22}is smaller than the voltage V

_{C11}+ V

_{in}, then the energy stored in the capacitor C

_{11}is transferred to capacitor C

_{22}through D

_{21}and switch S

_{b}. Similarly capacitor C

_{(k-1)1}transfers its energy to C

_{K2}when the voltage across capacitors C

_{12}+ C

_{22}+… + C

_{K2}is smaller than voltage V

_{in}+ V

_{C11}+ C

_{C21}+… + V

_{C(K-1)1}through diode D

_{K1}. In this mode the output voltage is equal to the input voltage (V

_{in}) + V

_{C11}+V

_{C21}+…+ V

_{CK1}.

_{a}is turned ON and switch S

_{b}is turned OFF, when the voltage across capacitor C

_{11}is smaller than capacitor C

_{12}, then capacitor C

_{11}is charged by capacitor C

_{12}through diode D

_{12}and switch S

_{a}. When the voltage across capacitor C

_{11}+ C

_{21}is smaller than the voltage across capacitor C

_{12}+ C

_{22}, then capacitor C

_{22}transfers its energy to capacitor C

_{21}through diode D

_{22}and switch S

_{a}. Similarly capacitor C

_{K2}transfers its energy to capacitor C

_{K1}through D

_{K2}when the voltage across capacitor C

_{11}+ C

_{21}+…+ C

_{k1}is smaller than the voltage C

_{12}+ C

_{22}+ C

_{K2}. In this mode the output voltage is equal to the input voltage (V

_{in}) + V

_{C12}+ V

_{C22}+ …+ V

_{CK2}.

#### 3.2. Voltage Gain Analysis of a Multistage Converter without Diode and Switches Loss

_{in}. The voltage conversion ratio or voltage gain is equal to the (K + 1) i.e., number of stages +1 and also depends on number of capacitors. Figure 16a,b depict the graphs of the required number of devices/components versus the number of stages in 2-dimensional and in 3-dimensional view, respectively. From Figure 16a,b it is observed that the number of devices/components linearly increases as the number of stages is increased. Thus, with each stage increase two more diodes and capacitors are needed. It is also observed that the number of diodes is equal to the number of capacitors.

_{C}and K

_{D}number of capacitor and diode used to design the proposed circuit. The graph of voltage gain versus number of stages is shown in Figure 17a. It is observed that the proposed converter with K stages provides a K + 1 voltage conversion ratio. The graph of the number of stage devices/components versus voltage gain is shown in Figure 17b. It is observed that the number of devices/components linearly increases as the voltage gain requirement is increased. Thus, two diodes and two capacitors need to be connected to increase voltage gain by a factor of 1. It is also observed that 2 K diodes and 2 K capacitors are required to attain a voltage gain K + 1.

_{o}/V

_{in}), number of stages (K) and duty cycle (D) is shown in Figure 17c. It is observed that two capacitors and two diodes are required to design one stage of the proposed converter. The graph of output voltage for stages 1 to 9 by considering an input voltage of 25 V is shown in Figure 17d. It is observed that the output voltage is increased as the number of stages increases, and each stage contributes a voltage equal to the input voltage (25 V) to an output voltage of the proposed converter.

#### 3.3. Voltage Gain Analysis of the Multistage Converter with Diode and Switches Loss

_{d}.

_{in}− 4V

_{d}except for the voltage across capacitor C

_{12}. The voltage across capacitor C

_{12}is equal to V

_{in}− 2V

_{d}. Thus, the proposed topology is self-balanced and magnetic component-free. The output voltage of the converter is limited by the devices’ forward voltage and number of devices.

_{d}= 1) and ideal diode is shown in Figure 18a. The graph of the proposed converter output voltage versus number of diodes or capacitors with a practical diode (V

_{d}= 1) and an ideal diode is shown in Figure 18b. From Figure 18a,b it is observed that the difference between the ideal and practical output voltage increases as the number of stages, diodes and capacitor requirement is increased. The difference between the ideal and practical output voltage depends on the number of stages of the proposed converter and it is equal to 4KV

_{d}as given in Equation (15).

## 4. Design Calculation of the Capacitors of the Proposed Converter

_{D}is the forward resistance of the diode, R

_{S}is the forward resistance of the switch, I

_{Sb}is the current through the switch S

_{b}and I

_{Sa}is the current through switch S

_{a}.

_{12}and C

_{11}is zero. Capacitor C

_{12}is charged through a resistance R

_{D}and R

_{S}from a supply voltage V

_{in}when switch S

_{b}is closed. The voltage across C

_{12}does not increase to V

_{in}instantaneously, but builds up exponentially and not linearly.

_{11}is charged through a resistance R

_{D}and R

_{S}from a capacitor C

_{12}voltage when switch S

_{a}is closed. Thus, when switch S

_{a}is closed capacitors C

_{11}and C

_{12}is charging and discharging, respectively.

_{11}and C

_{12}at any instant during charging is cycled as given in Equations (25) and (26) where, ${\mathrm{V}}_{\mathrm{C}{\prime}_{11}}$ and ${\mathrm{V}}_{\mathrm{C}{\prime}_{12}}$ is the initial voltage of capacitor C

_{11}and C

_{12}. If the initial storage voltage of C

_{11}and C

_{12}is positive:

_{11}and C

_{12}is negative:

_{12}to attain any value of V

_{C12}during the charging cycle is given in Equations (27) and (28).

_{11}to attain any value of V

_{C11}during the charging cycle is given in Equations (29) and (30).

## 5. Comparison of Proposed Converter with Recent DC-DC Inductor-less Converters

## 6. Experimental and Simulation Results of the Proposed Self-Balanced and Magnetic Component-Free Multistage DC-DC Converter

_{a}(here S

_{1}) and S

_{b}(here S

_{2}) are operated complementarily with a 50% duty cycle. High switching frequency is used to reduce the rating of the capacitor.

_{D}+ R

_{S}) C as explained in Section 4. The output power waveform and switch voltage are shown in Figure 22a,b, respectively. The output voltage and input voltage waveform with ideal components (voltage drop across the switch and the diode is zero) are shown in Figure 22c. The output voltage and input voltage waveform (assuming a 1 V voltage drop across the switch and diode) are shown in Figure 22d.

## 7. Conclusions

- (i)
- Magnetic component-free (transformer-less and inductor-less)
- (ii)
- Continuous input current
- (iii)
- Low voltage rating semiconductor devices and capacitors
- (iv)
- Modularity
- (v)
- Easy to add a higher number of levels to increase the voltage
- (vi)
- Only two control switches with alternating operation and simple control are needed.

## Author Contributions

## Conflicts of Interest

## References

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**Figure 1.**Photovoltaic Central Inverter Structure (PV-CIS) for transfer of PV energy to an electric grid.

**Figure 2.**Photovoltaic String Inverter Structure (PV-SIS) for transfer of PV energy to the electric grid.

**Figure 3.**(

**a**) Photovoltaic AC Module Structure (PV-ACMS); (

**b**) Photovoltaic Multi-String Inverter Structure (PV-MSIS) for transfer of PV energy to the electric grid.

**Figure 4.**Inductive networks: (

**a**) Switched Inductor; (

**b**) Voltage Lift switched Inductor cell; (

**c**) modified voltage lift switched inductive cell.

**Figure 5.**Proposed multistage self-balanced and magnetic component-free DC-DC converter in a photovoltaic system for the transfer of photovoltaic energy to a DC load, grid or motor.

**Figure 6.**(

**a**) Power- voltage or current- voltage graphs of a photovoltaic system; (

**b**) MPPT when ∆P = 0 and ∆V = 0; (

**c**) MPPT when ∆P < 0 and ∆V < 0; (

**d**) MPPT when ∆P > 0 and ∆V > 0; (

**e**) MPPT when ∆P > 0 and ∆V < 0; (

**f**) MPPT when ∆P < 0 and ∆V > 0.

**Figure 7.**(

**a**) Three–Level Series-Parallel Switched Capacitor (Series-Parallel SC) Converter; (

**b**) Flying Capacitor Multilevel DC-DC Converter (FCMDC).

**Figure 16.**Number of devices/components versus the number of stages (

**a**) 2-dimensional view; (

**b**) 3-dimensional view.

**Figure 17.**Relations of converter parameters: (

**a**) graph of voltage gain versus number of stages; (

**b**) graph of the number of devices/component versus voltage gain; (

**c**) graph of the voltage gain (V

_{o}/V

_{in}), number of stages (K) and duty cycle (D); (

**d**) output voltage for stage 1 to 9 for 25 V input voltage.

**Figure 18.**Comparison graph considering V

_{in}= 24 V. (

**a**) Graph of converter output voltage versus number of stages (practical and ideal diode); (

**b**) graph of converter output voltage versus number of diodes or capacitors (practical and ideal diode).

**Figure 19.**(

**a**) Power circuit of the 1-stage proposed converter; (

**b**) equivalent circuit of 1-stage proposed converter when S

_{b}is ON; (

**c**) equivalent circuit of 1-stage proposed converter when S

_{a}is ON.

**Figure 20.**Comparison of the proposed converter with recent transformer-less and inductor-less converters (Discussed in Section 2) (

**a**) Graph of the number of switches versus number of levels/stages; (

**b**) graph of the number of diodes versus number of levels/stages; (

**c**) graph of the number of capacitors versus number of levels/stages; (

**d**) graph of the voltage conversion ratio versus number of levels/stages. (A: SPSC, B: FCMDC, C: MMDC, D: Fibonacci, E: switch mode, F: MMCCC, G: proposed converter).

**Figure 21.**Simulation results (

**a**) Output voltage and current waveform with ideal components and V

_{in}= 24 V; (

**b**) Output voltage and current waveform with practical components and V

_{in}= 24 V.

**Figure 22.**Simulation results (

**a**) Output power of proposed converter; (

**b**) Gate pulses to control switches of the converter and drain to source of the converter; (

**c**) Output voltage and input voltage waveform with ideal components; (

**d**) Output voltage and input voltage waveform with practical components; (

**e**) Voltage across diode D

_{11}, D

_{21}, D

_{31}and D

_{41}; (

**f**) Voltage across diode D

_{12}, D

_{22}, D

_{32}and D

_{42}.

**Figure 23.**Voltage across capacitor C

_{41}, C

_{31}, C

_{21}C

_{11}, C

_{42}, C

_{32}, C

_{22}and C

_{12}(Top to bottom in figure).

**Figure 25.**(

**a**) PIC controller output; (

**b**) TLP 250 gate driver output; (

**c**) Output voltage and input voltage waveform; (

**d**) Output current waveforms.

**Figure 26.**Capacitors voltage (

**a**) C

_{11}(

**b**) C

_{12}(

**c**) C

_{21}(

**d**) C

_{22}(

**e**) C

_{31}(

**f**) C

_{32}(

**g**) C

_{41}(

**h**) C

_{42}.

**Figure 27.**Voltage across diodes (

**a**) D

_{11}(

**b**) D

_{12}(

**c**) D

_{21}(

**d**) D

_{22}(

**e**) D

_{31}(

**f**) D

_{32}(

**g**) D

_{41}(

**h**) D

_{42}.

Operation Mode | Switches State | Capacitors of Left Part (Section-I) | Capacitors of Right Part (Section-II) | |||||||
---|---|---|---|---|---|---|---|---|---|---|

S1 | S2 | S3 | S4 | S5 | S6 | S7 | S8 | |||

Mode-I | OFF | ON | OFF | ON | ON | OFF | ON | OFF | Charging | Discharging |

Mode-II | OFF | OFF | OFF | OFF | ON | OFF | ON | OFF | No action | Discharging |

Mode-III | ON | OFF | ON | OFF | OFF | ON | OFF | ON | Discharging | Charging |

Mode-III | ON | OFF | ON | OFF | OFF | OFF | OFF | OFF | Discharging | No Action |

Converter Type | Number of Levels/Stages | ||||||||
---|---|---|---|---|---|---|---|---|---|

1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | N | |

SPSC | 1 | 4 | 7 | 10 | 13 | 16 | 19 | 22 | 3N − 2 |

FCMDC | 2 | 4 | 6 | 8 | 10 | 12 | 14 | 16 | 2N |

MMDC | 2 | 6 | 12 | 20 | 30 | 42 | 56 | 72 | N(N + 1) |

Fibonacci | 4 | 7 | 10 | 13 | 16 | 19 | 22 | 25 | 3N + 1 |

Switch Mode | 4 | 8 | 12 | 16 | 20 | 24 | 28 | 32 | 4N |

MMCCC | 1 | 4 | 7 | 10 | 13 | 16 | 19 | 22 | 3N − 2 |

Proposed | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 |

Converter Type | Number of Levels | ||||||||
---|---|---|---|---|---|---|---|---|---|

1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | N | |

SPSC | 1 | 4 | 7 | 10 | 13 | 16 | 19 | 22 | 3N − 2 |

FCMDC | 2 | 4 | 6 | 8 | 10 | 12 | 14 | 16 | 2N |

MMDC | 2 | 6 | 12 | 20 | 30 | 42 | 56 | 72 | N(N + 1) |

Fibonacci | 4 | 7 | 10 | 13 | 16 | 19 | 22 | 25 | 3N + 1 |

Switch Mode | 4 | 6 | 8 | 10 | 12 | 14 | 16 | 18 | 2N + 2 |

MMCCC | 1 | 4 | 7 | 10 | 13 | 16 | 19 | 22 | 3N − 2 |

Proposed | 2 | 4 | 6 | 8 | 10 | 12 | 14 | 16 | 2N |

Converter Type | Number of Levels | ||||||||
---|---|---|---|---|---|---|---|---|---|

1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | N | |

SPSC | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | N |

FCMDC | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | N |

MMDC | 1 | 3 | 6 | 10 | 15 | 21 | 28 | 36 | N(N + 1)/2 |

Fibonacci | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | N |

Switch Mode | 3 | 5 | 7 | 9 | 11 | 13 | 15 | 17 | 2N + 1 |

MMCCC | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | N |

Proposed | 2 | 4 | 6 | 8 | 10 | 12 | 14 | 16 | 2N |

Converter Type | Number of Levels | ||||||||
---|---|---|---|---|---|---|---|---|---|

1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | N | |

SPSC | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | N |

FCMDC | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | N |

MMDC | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | N |

Fibonacci | 1 | 3 | 5 | 8 | Not feasible to design for higher levels | ||||

Switch Mode | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | N + 1 |

MMCCC | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | N |

Proposed | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | N + 1 |

**Table 6.**Cost of the proposed and recent DC-DC converters (discussed in Section 2).

Converter | Cost of the Converter |
---|---|

SPSC | (3N − 2) (Cost of each switch + cost of each diode) + N (cost of each capacitor) |

FCMDC | 2N (Cost of each switch + cost of each diode) + N (cost of each capacitor) |

MMDCC | N(N + 1){(Cost of each switch + cost of each diode) + 0.5 (cost of each capacitor)} |

Fibonacci | (3N + 1) (Cost of each switch + cost of each diode) +N (cost of each capacitor) |

Switch Mode | 4N (Cost of each switch) + 2(N + 1)(cost of each diode) + (2N + 1) (cost of each capacitor) |

MMCCC | (3N − 2) (Cost of each switch + cost of each diode) + N (cost of each capacitor) |

Proposed | 2 (Cost of each switch) +2N (cost of each diode + cost of each capacitor) |

Sr/No | Components | Value | No. of Components |
---|---|---|---|

1 | Switch (S_{1} and S_{2}) | IRF250 (0.085 ON sate resistance) | 2 |

2 | Diodes | BYQ28E | 8 |

3 | Capacitors | 220 μF, 50 V | 8 |

4 | Load | 168 Ω, 60 W | 1 |

5 | Gate Driver IC | TLP250 | 2 |

© 2017 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Bhaskar, M.S.; Padmanaban, S.; Blaabjerg, F.
A Multistage DC-DC Step-Up Self-Balanced and Magnetic Component-Free Converter for Photovoltaic Applications: Hardware Implementation. *Energies* **2017**, *10*, 719.
https://doi.org/10.3390/en10050719

**AMA Style**

Bhaskar MS, Padmanaban S, Blaabjerg F.
A Multistage DC-DC Step-Up Self-Balanced and Magnetic Component-Free Converter for Photovoltaic Applications: Hardware Implementation. *Energies*. 2017; 10(5):719.
https://doi.org/10.3390/en10050719

**Chicago/Turabian Style**

Bhaskar, Mahajan Sagar, Sanjeevikumar Padmanaban, and Frede Blaabjerg.
2017. "A Multistage DC-DC Step-Up Self-Balanced and Magnetic Component-Free Converter for Photovoltaic Applications: Hardware Implementation" *Energies* 10, no. 5: 719.
https://doi.org/10.3390/en10050719