# High Efficiency Solar Power Generation with Improved Discontinuous Pulse Width Modulation (DPWM) Overmodulation Algorithms

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## Abstract

**:**

## 1. Introduction

## 2. Equivalent Circuit of a PV Power System

#### 2.1. Perturbation and Observation (P&O) MPPT Algorithm

#### 2.2. A Boost DC-DC Converter and the Equivalent Circuit

#### 2.3. Division of the Overmodulation Area

#### 2.4. Full Modulation Region Voltage Vector

## 3. DPWM Overmodulation Algorithm

## 4. Simulation and Experimental Validation of the Proposed Scheme

^{2}; the parameters of a single photovoltaic module are presented in Table 4. The output voltage range of the DC/DC converter (5 kW) is 100‒400 V. The power module model of the DC/AC converter (2 kW) is PM30RSF060 (as shown in Figure 10c), and its maximum switching frequency is 20 kHz.

#### 4.1. Simulation Results of Different Varied Solar Irradiations

#### 4.2. DC/AC under the DPWM scheme

## 5. Conclusions

- (i)
- A P&O MPPT algorithm is applied to a boost DC/DC converter so as to effectively harvest solar energy and transform to DC electricity;
- (ii)
- A novel control technology is proposed, combining discontinuous pulse width modulation (DPWM) and overmodulation technology to better utilize the DC-link voltage.
- (iii)
- It has been shown by measurements that through implementing this algorithm, the switching losses in the power electronic devices are reduced.
- (iv)
- The test results have confirmed that the DPWM overmodulation algorithm can effectively reduce harmonic distortion of the three-phase output voltage and current. It has also improved the conversion efficiency of photovoltaic systems.
- (v)
- The proposed technology is simple to implement in practical PV inverters as there are no alterations to existing hardware design. It may also be applied to other grid-tie inverters to improve their performance.

## Author Contributions

## Funding

## Conflicts of Interest

## Nomenclature

$\alpha $ | Angle between the output voltage vector and the horizontal axis |

${\alpha}_{\gamma}$ | Angle between the intersection of the output voltage vector and the hexagon boundary, and the vertex of hexagon |

${\alpha}_{h}$ | Control angle to determine how long the output voltage vector stays at the vertex of hexagon |

${\mathsf{\gamma}}_{IL}$ | Current ripple factor of the inductor |

${\gamma}_{V}{}_{O}$ | Voltage ripple factor of the inductor |

${C}_{i}$, | Capacitance of the input capacitor in DC/DC converter |

${C}_{o}$, | Capacitance of the output capacitor in DC/DC converter |

$D$ | Duty ratio of DC/DC converter |

$f$ | Switching frequency of a DC/DC converter |

${i}_{a}$, ${i}_{b}$, ${i}_{c}$ | Inverter output currents |

${I}_{mpp}$ | Equivalent output current at maximum power point |

L | Filter inductance |

${L}_{L}$ | Symmetrical load inductance |

${L}^{\prime}$ | Inductance of a DC/DC converter |

m | Modulation coefficient |

N | Sector |

${p}_{mpp}$ | Maximum power of a PV module |

R | Filter inductance |

R_{L} | Symmetrical load resistance |

${R}_{mpp}$ | Equivalent resistance at maximum power point |

${R}_{O}$ | Load resistance of the DC/DC converter |

S | Sector number |

${T}_{1}$,${T}_{2}$,$\text{}{T}_{0}$ | Action time of adjacent fundamental voltage vectors and zero vector |

${T}_{s}$ | Switching period |

${u}_{0}~{u}_{7}$ | Basic voltage space vectors |

${U}_{\alpha}$,${U}_{\beta}$ | Two components of the output voltage vector in the $\alpha -\beta $ coordinates |

${U}_{d}$ | DC-link voltage |

${u}_{m}$ | Amplitude of the phase voltage |

${u}_{m\_max}$ | Maximum phase voltage in linear modulation area |

${U}_{out}$ | Output voltage |

${V}_{mpp}$ | Equivalent output voltage at maximum power point |

${V}_{O}$ | Load voltage of the DC/DC converter |

${t}_{rN}$ | Turn-on time |

${t}_{fN}$ | Turn-off time |

${f}_{s}$ | Switching frequency of power devices |

${I}_{CN}$ | Forward current of IGBT |

${I}_{CM}$ | Amplitude of the sinusoidal current |

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**Figure 11.**The performance of the DC/DC converter with varied solar irradiation. (

**a**) Varied solar irradiation; (

**b**) the output voltage at maximum power point (MPP); (

**c**) the output current at MPP; (

**d**) the output power at MPP.

**Figure 14.**Modulation waveforms under different modulation schemes. (

**a**) Space vector pulse width modulation (SVPWM); (

**b**) DPWM (m = 0.778); (

**c**) DPWM (m = 0.916); (

**d**) DPWM (m = 1).

No. | Scenario | Example Route | Action |
---|---|---|---|

1 | ${P}_{current}>{P}_{previous}\text{}\text{}{V}_{current}{V}_{previous}$ | A → B | Increase voltage |

2 | ${P}_{current}>{P}_{previous}\text{}\text{}{V}_{current}{V}_{previous}$ | D → C | Decrease voltage |

3 | ${P}_{current}<{P}_{previous}\text{}\text{}{V}_{current}{V}_{previous}$ | C → D | Decrease voltage |

4 | ${P}_{current}<{P}_{previous}\text{}\text{}{V}_{current}{V}_{previous}$ | B → A | Increase voltage |

S | 1 | 2 | 3 | 4 | 5 | 6 |
---|---|---|---|---|---|---|

Sector N | II | VI | I | IV | III | V |

Action condition | Sector N | S for the 30° | Sector |
---|---|---|---|

$\frac{{U}_{\beta}}{{U}_{\alpha}}<\mathrm{tan}\left(\frac{\mathsf{\pi}}{6}\right)$ | I | 3 (True) | 9 (False) |

IV | 10 (True) | 4 (False) | |

${U}_{\alpha}>0$ | II | 1 (True) | 7 (False) |

V | 6 (True) | 12 (False) | |

$\frac{{U}_{\beta}}{{U}_{\alpha}}<-\mathrm{tan}\left(\frac{\mathsf{\pi}}{6}\right)$ | III | 11 (True) | 5 (False) |

VI | 2 (True) | 8 (False) |

Open-Circuit Voltage (V) | Short-Circuit Current (A) | Max Voltage (V) | Max Current (A) | Max Power (W) |
---|---|---|---|---|

45.2 | 5.36 | 37.1 | 5.11 | 190 |

Harmonics | SVPWM | DPWM |
---|---|---|

5th | 3.55% | 0.93% |

7th | 4.84% | 3.68% |

11th | 1.61% | 0 |

THD | 6.58% | 4.40% |

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## Share and Cite

**MDPI and ACS Style**

Li, L.; Wang, H.; Chen, X.; Bukhari, A.A.S.; Cao, W.; Chai, L.; Li, B. High Efficiency Solar Power Generation with Improved Discontinuous Pulse Width Modulation (DPWM) Overmodulation Algorithms. *Energies* **2019**, *12*, 1765.
https://doi.org/10.3390/en12091765

**AMA Style**

Li L, Wang H, Chen X, Bukhari AAS, Cao W, Chai L, Li B. High Efficiency Solar Power Generation with Improved Discontinuous Pulse Width Modulation (DPWM) Overmodulation Algorithms. *Energies*. 2019; 12(9):1765.
https://doi.org/10.3390/en12091765

**Chicago/Turabian Style**

Li, Lan, Hao Wang, Xiangping Chen, Abid Ali Shah Bukhari, Wenping Cao, Lun Chai, and Bing Li. 2019. "High Efficiency Solar Power Generation with Improved Discontinuous Pulse Width Modulation (DPWM) Overmodulation Algorithms" *Energies* 12, no. 9: 1765.
https://doi.org/10.3390/en12091765