# New Fast MPPT Method Based on a Power Slope Detector for Single Phase PV Inverters

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Converter Modeling

## 3. DC-Bus Voltage Modulation and PV Efficiency

## 4. Proposed P-V Slope Detector

## 5. Maximum Power Point Tracking Based on the P-V Slope Detector

^{©}, with the proposed PSD-MPPT and parameters given in Table 2 and Table 3. Figure 11 shows the simulation results against irradiance step changes between 250 W/m${}^{2}$ and 1 kW/m${}^{2}$ every 125 ms. The figure shows, from top to bottom: ${i}_{\mathrm{pv}}$, ${v}_{\mathrm{pv}}$, ${p}_{\mathrm{pv}}$, currents ${i}_{j}$ through the inductors (${i}_{1}$, ${i}_{2}$, and ${i}_{3}$), ${p}_{m}$ and ${v}_{m}$ extracted by the band-pass filters, parameter $\delta $, duty-cycle d, DC-bus voltage ${v}_{\mathrm{dc}}$, and the inverter’s output current and voltage. The converter starts up and takes only 50 ms to find the MPP at maximum irradiance. Every new MPP is found in approximately 50 ms. The calculated PV efficiency at maximum irradiance is $\eta =100\xb7402.9/403.6=99.83$%. It should be noted that inductors currents ${i}_{j}$ show safe values and are equalized despite not using a current control on each converter module.

## 6. Modification for Power Reference Tracking

^{©}, and the results are presented in Figure 16 and Figure 17, both at maximum irradiance. Specifically, Figure 16 shows the control performance against reference steps between 200 W and 500 W. The converter takes approximately 50 ms to shift from medium power to MPP and vice versa. On the other hand, Figure 17 shows the simulation results against reference changes between 0 W and 500 W. This is a more challenging case, because the null power regulation at the open-circuit voltage presents the lowest stability margins and because duty-cycle transitions here are the widest possible. Transients take 70 ms from zero power to MPP and 25 ms from MPP to null power. It should be noted again that the currents ${i}_{j}$ of all three boost modules are equalized and do not present peaks during transients.

## 7. Experimental Results

## 8. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

- Sajadian, S.; Ahmadi, R.; Zargarzadeh, H. Extremum Seeking-Based Model Predictive MPPT for Grid-Tied Z-Source Inverter for Photovoltaic Systems. IEEE J. Emerg. Sel. Top. Power Electron.
**2019**, 7, 1904–1914. [Google Scholar] [CrossRef] - Pahari, O.P.; Subudhi, B. Integral sliding mode-improved adaptive MPPT control scheme for suppressing grid current harmonics for PV system. IET Renew. Power Gener.
**2018**, 12, 216–227. [Google Scholar] [CrossRef] - Kumar, N.; Hussain, I.; Singh, B.; Panigrahi, B.K. Normal Harmonic Search Algorithm-Based MPPT for Solar PV System and Integrated With Grid Using Reduced Sensor Approach and PNKLMS Algorithm. IEEE Trans. Ind. App.
**2018**, 54, 6343–6352. [Google Scholar] [CrossRef] - Sangwongwanich, A.; Blaabjerg, F. Mitigation of Interharmonics in PV Systems With Maximum Power Point Tracking Modification. IEEE Trans. Power Electron.
**2019**, 34, 8279–8282. [Google Scholar] [CrossRef] - Rezk, H.; Aly, M.; Al-Dhaifallah, M.; Shoyama, M. Design and Hardware Implementation of New Adaptive Fuzzy Logic-Based MPPT Control Method for Photovoltaic Applications. IEEE Access
**2019**, 7, 106427–106438. [Google Scholar] [CrossRef] - Gonzalez-Medina, R.; Liberos, M.; Marzal, S.; Figueres, E.; Garcera, G. A Control Scheme without Sensors at the PV Source for Cost and Size Reduction in Two-Stage Grid Connected Inverters. Energies
**2019**, 12, 2955. [Google Scholar] [CrossRef] - Chandra Mouli, G.R.; Schijffelen, J.H.; Bauer, P.; Zeman, M. Design and Comparison of a 10-kW Interleaved boost Converter for PV Application Using Si and SiC Devices. IEEE J. Emerg. Sel. Top. Power Electron.
**2017**, 5, 610–623. [Google Scholar] [CrossRef] - Ho, C.N.; Breuninger, H.; Pettersson, S.; Escobar, G.; Serpa, L.A.; Coccia, A. Practical Design and Implementation Procedure of an Interleaved boost Converter Using SiC Diodes for PV Applications. IEEE Trans. Power Electron.
**2012**, 27, 2835–2845. [Google Scholar] [CrossRef] - Ahmed, J.; Salam, Z. An Enhanced Adaptive P&O MPPT for Fast and Efficient Tracking Under Varying Environmental Conditions. IEEE Trans. Sustain. Energy
**2018**, 9, 1487–1496. [Google Scholar] - Ahmed, J.; Salam, Z. A Modified P&O Maximum Power Point Tracking Method With Reduced Steady-State Oscillation and Improved Tracking Efficiency. IEEE Trans. Sustain. Energy
**2016**, 4, 1506–1515. [Google Scholar] - Macaulay, J.; Zhou, Z. A Fuzzy Logical-Based Variable Step Size P&O MPPT Algorithm for Photovoltaic System. Energies
**2018**, 11, 1340. [Google Scholar] - Li, C.; Chen, Y.; Zhou, D.; Liu, J.; Zeng, J. A High-Performance Adaptive Incremental Conductance MPPT Algorithm for Photovoltaic Systems. Energies
**2016**, 9, 288. [Google Scholar] [CrossRef] - Espi, J.M.; Castello, J. A Novel Fast MPPT Strategy for High Efficiency PV Battery Chargers. Energies
**2019**, 12, 1152. [Google Scholar] [CrossRef] - Galiano, I.; Ordonez, M. PV Energy Harvesting Under Extremely Fast Changing Irradiance: State-Plane Direct MPPT. IEEE Trans. Ind. Electron.
**2019**, 66, 1852–1861. [Google Scholar] - Paz, F.; Ordonez, M. High-Performance Solar MPPT Using Switching Ripple Identification Based on a Lock-In Amplifier. IEEE Trans. Ind. Electron.
**2016**, 63, 3595–3604. [Google Scholar] [CrossRef] - Sangwongwanich, A.; Yang, Y.; Blaabjerg, F.; Wang, H. Benchmarking of Constant Power Generation Strategies for Single-Phase Grid-Connected Photovoltaic Systems. IEEE Trans. Ind. App.
**2018**, 54, 447–457. [Google Scholar] [CrossRef]

**Figure 1.**PV inverter, where the DC-DC converter is implemented using N interleaved boost converters.

**Figure 5.**Resulting PV power modulation at different operating points: at the left of the MPP (red, with ${\tilde{p}}_{\mathrm{pv}}$ and ${\tilde{v}}_{\mathrm{pv}}$ in phase), at the right of the MPP (green, with ${\tilde{p}}_{\mathrm{pv}}$ and ${\tilde{v}}_{\mathrm{pv}}$ in anti-phase), and at the MPP (blue, where ${\tilde{p}}_{\mathrm{pv}}$ doubles the frequency of ${\tilde{v}}_{\mathrm{pv}}$).

**Figure 8.**Performance of the band-pass filter ${G}_{\mathrm{BP}}\left(z\right)$: (

**a**) frequency response; and (

**b**) step response.

**Figure 9.**Transients produced by a fast change in power: (

**a**) calculated AC power ${p}_{m}$; (

**b**) slope detector output $\delta $.

**Figure 11.**Simulated results of the proposed MPPT method against irradiance steps between 250 W/m${}^{2}$ and 1 kW/m${}^{2}$. The static efficiency at 1 kW/m${}^{2}$ is 99.83%.

**Figure 13.**Performance of the proposed power control: (

**a**) when the requested power is higher than available PV power; (

**b**) when requested power is lower than available PV power.

**Figure 15.**Resulting open-loop Bode diagrams when operating at: (

**a**) ${V}_{\mathrm{pv}}={V}_{\mathrm{oc}}$ with a single active module (worst-case dynamics); and (

**b**) ${V}_{\mathrm{pv}}={V}_{\mathrm{MPP}}$ with the three modules activated. PM, phase margin; GM, gain margin.

**Figure 16.**Simulated results at a constant irradiance of 1 kW/m${}^{2}$ with power reference step changes between 200 W and 500 W.

**Figure 17.**Simulated results at a constant irradiance of 1 kW/m${}^{2}$ with power reference step changes between 0 W and 500 W.

**Figure 18.**Operating point shift during irradiance step changes: (

**a**) time plot of power; and (

**b**) P-V plot. The converter is switched on at PV1, and then, irradiance is changed to PV2, PV3, and PV4. The converter is finally switched off at PV4 (sample time = 2 ms).

**Figure 19.**Detailed transient responses against irradiance steps: (

**a**) from PV1 to PV4; and (

**b**) from PV4 to PV1. Ch1: PV current (2 A/div). Ch2: PV voltage (10 V/div). Ch4: DC-bus voltage (50 V/div). Math: PV power (200 W/div).

**Figure 20.**Response against power reference steps between 200 W and 500 W: (

**a**) at the PV module, where Ch1 is the PV current (5 A/div), Ch2 is the PV voltage (10 V/div), CH4 is a power reference synchronism, and Math is the PV power (200 W/div); (

**b**) at the inverter side, where Ch1 is the transformer’s current (5 A/div), Ch2 is the reduced grid voltage (200 V/div), Ch3 is the DC-bus voltage (50 V/div), and CH4 is the power reference synchronism.

**Figure 21.**Response against power reference steps between 0 W and 500 W: (

**a**) at the PV module, where Ch1 is the PV current (5 A/div), Ch2 is the PV voltage (10 V/div), CH4 is a power reference synchronism, and Math is the PV power (200 W/div); (

**b**) at the inverter side, where Ch1 is the transformer’s current (5 A/div), Ch2 is the reduced grid voltage (200 V/div), Ch3 is the DC-bus voltage (50 V/div), and CH4 is the power reference synchronism.

**Figure 22.**Start-up process of the PV inverter. Ch1: PV current (2 A/div). Ch2: PV voltage (10 V/div). Ch4: DC-bus voltage (50 V/div). Math: PV power (200 W/div).

**Figure 23.**Activation/deactivation of parallelized converters: (

**a**) turn-on of Converter 2 and current sharing with Converter 1; (

**b**) turn-off of Converter 2 and all power is handled by Converter 1. Ch1: Converter 1 input current (2 A/div). Ch2: Converter 2 input current (2 A/div). Ch3: PV current (2 A/div). Ch4: on/off synchronism.

Description | Variable | Value |
---|---|---|

Number of PV modules in series | ${n}_{s}$ | 3 |

Number cells/module | ${n}_{c}$ | 36 |

Open-circuit voltage @ 1kW/m${}^{2}$ | ${V}_{\mathrm{OC}}$ | 65 V |

Short-circuit current @ 1kW/m${}^{2}$ | ${I}_{\mathrm{SC}}$ | 8.5 A |

Maximum power point voltage @ 1kW/m${}^{2}$ | ${V}_{\mathrm{MPP}}$ | 55.5 V |

Maximum power point current @ 1kW/m${}^{2}$ | ${I}_{\mathrm{MPP}}$ | 7.6 V |

Efficiency @ ${\tilde{v}}_{\mathrm{dc}}$ = 2% peak-peak | ${\eta}_{|2\%}$ | 99.94% |

Efficiency @ ${\tilde{v}}_{\mathrm{dc}}$ = 4% peak-peak | ${\eta}_{|4\%}$ | 99.78% |

Efficiency @ ${\tilde{v}}_{\mathrm{dc}}$ = 6% peak-peak | ${\eta}_{|6\%}$ | 99.44% |

Efficiency @ ${\tilde{v}}_{\mathrm{dc}}$ = 8% peak-peak | ${\eta}_{|8\%}$ | 99.09% |

Efficiency @ ${\tilde{v}}_{\mathrm{dc}}$ = 10% peak-peak | ${\eta}_{|10\%}$ | 98.50% |

Description | Variable | Value |
---|---|---|

Number of boost converters | N | 3 |

Nominal power | P | 450 W |

Switching frequency | ${f}_{sw}$ | 10 kHz |

DC-bus voltage | ${V}_{\mathrm{dc}}$ | 150 V |

DC-bus capacitance | ${C}_{\mathrm{dc}}$ | 1470 $\mathsf{\mu}$F |

Input filter inductances | ${L}_{j}$ | 1200 $\mathsf{\mu}$H |

Inductor series resistances | ${r}_{j}$ | 25 m$\mathsf{\Omega}$ |

Input capacitance | C | 470 $\mathsf{\mu}$F |

Description | Variable | Value |
---|---|---|

Sampling frequency | ${f}_{s}=\frac{1}{T}$ | 20/11 kHz |

Slope detector’s gain | ${k}_{m}$ | 2500 |

Bandpass filters, center-frequency | ${f}_{0}$ | 100 Hz |

Bandpass filters, bandwidth | ${f}_{\mathrm{BW}}$ | 100 Hz |

Integrator’s gain | ${k}_{i}$ | 2 rad/s |

Power gain (power control) | ${k}_{p}$ | 0.01 |

Minimum PV current for start-up | ${i}_{\mathrm{min}}$ | 50 mA |

© 2019 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**

Espi, J.M.; Castello, J.
New Fast MPPT Method Based on a Power Slope Detector for Single Phase PV Inverters. *Energies* **2019**, *12*, 4379.
https://doi.org/10.3390/en12224379

**AMA Style**

Espi JM, Castello J.
New Fast MPPT Method Based on a Power Slope Detector for Single Phase PV Inverters. *Energies*. 2019; 12(22):4379.
https://doi.org/10.3390/en12224379

**Chicago/Turabian Style**

Espi, Jose Miguel, and Jaime Castello.
2019. "New Fast MPPT Method Based on a Power Slope Detector for Single Phase PV Inverters" *Energies* 12, no. 22: 4379.
https://doi.org/10.3390/en12224379