# Novel Incremental Conductance Feedback Method with Integral Compensator for Maximum Power Point Tracking: A Comparison Using Hardware in the Loop

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

_{2}emissions and boost the proportion of renewable energy, with solar power being a prominent area of investigation in the recent literature. Techniques are being developed to optimize the energy recovered from PV cells and increase system efficiency, including modeling PV cells, the use of converter topologies to connect PV systems to high-power inverters, and the use of MPPT methods. Certain MPPT algorithms are intricate and demand high processing power. The literature describes several MPPT methods; however, the number of hardware resources required by MPPT algorithms is typically not disclosed. This work proposes a novel MPPT technique based on integral feedback conductance and incremental conductance error, considering the current dynamics of the boost converter. This MPPT algorithm is compared to the most widely used techniques in the literature and evaluates each method’s efficiency, performance, and computational needs using an HIL system. Comparisons are made with well-known MPPT algorithms, such as perturb and observe, incremental conductance, and newer techniques based on fuzzy logic and neural networks (NNs). As the NN that is most widely used in the literature depends on irradiation and temperature, an additional NN that is trained using the proposed method is also investigated.

## 1. Introduction

_{2}emissions from fossil fuels. As a result, researchers are continuously seeking new methods of maximizing the power production of solar panels [1,2]. Using wide-bandgap semiconductors, such as silicon carbide or gallium nitride [3], and lowering computing demands [4] are two further ways to improve the effectiveness of renewable energy systems.

## 2. Review of PV Model and MPPT Control Methods

#### 2.1. Mathematical Model of Solar Panels

- ${I}_{sc}$—the short circuit current under Standard Test Conditions (STC) (model first parameter)
- ${K}_{l}$—the short circuit temperature coefficient
- ${T}_{c}$—the cell temperature
- ${T}_{r}$—the reference temperature (298.15 K)
- $G$—solar irradiance
- ${G}_{STC}$—solar irradiance STC

- ${I}_{0}$—the diode saturation current (second parameter of the model)
- $q$—the electron charge constant ($1.6\times {10}^{-19}$)
- ${V}_{d}$—the diode voltage
- $A$—the ideal factor of the diode (third parameter of the model)
- $k$—Boltzmann’s constant ($1.38\times {10}^{-23}$)

- ${V}_{PV}$—the photovoltaic cell voltage
- ${I}_{PV}$—the photovoltaic cell current
- ${R}_{S}$—the series resistance of the solar panel (fourth model parameter)
- ${R}_{sh}$—the parallel or shunt resistance of the solar panel (fifth model parameter).

_{oc}(open circuit voltage), I

_{sc}(short circuit current), V

_{MPP}, I

_{MPP}, and voltage, as well as the temperature coefficients (K

_{v}, K

_{i}) [36]. According to [34,37], some methods can be used to model a PV cell when the coefficients are not disclosed.

#### 2.2. Review of MPPT Control Methods

#### 2.2.1. Perturb and Observe (P&O)

#### 2.2.2. Incremental Conductance (INC)

#### 2.2.3. Fuzzy Logic (FL)

#### 2.2.4. Artificial Neural Network (ANN)

^{2}and 1000 W/m

^{2}with steps of 50 W/m

^{2}, and at temperatures between 0 °C and 80 °C with steps of 5 °C. Although the PV equations produce non-linear I-V and P-V characteristics, the current values in the MPP have a linear relationship with irradiance and temperature (Figure 7), making the problem straightforward. In this case, only one hidden layer with 10 neurons was needed. This implementation achieved good results.

## 3. Incremental Conductance with Integral Compensator (IC-INC)

#### 3.1. Converter Topology

_{in}at the PV panel output (Figure 8) to reduce the voltage variation around the MPP. The converter controls the extracted current/power from the PV panel by varying the duty cycle, or by using a hysteretic controller if current control is used. In this work, for ANN and IC-INC, we chose to use hysteretic controllers, while for P&O, INC, and FL, we used a PWM modulator and duty-cycle variation.

_{sw}switching boost converter stores energy in the inductor L before releasing it in the output capacitor C

_{out}at higher voltage. The high-frequency voltage ripple in the PV (V

_{PV}) should be as minimal as possible, as the MPP is dependent on voltage and current, and oscillations in voltage or current around the MPP can cause a loss of power. Hence, the input capacitor should have enough energy to keep the PV voltage nearly constant during the high-frequency switching period and during abrupt irradiance changes.

_{PV}); thus, the ${I}_{PV}$ current will also present very little rippling, preventing limit cycles around the MPPT. The ${C}_{in}$ capacitor keeps the PV voltage and current nearly constant during the switching period.

#### 3.2. IC-INC Method and Algorithm

#### 3.3. Using the IC-INC Method to Train a Neural Network

^{−7}and an R of 0.85. The implementation with four hidden layers achieved an MSE of 2.48 × 10

^{−7}and an R of 0.92.

## 4. Results

#### 4.1. Laboratory Setup

#### 4.2. Test Results

^{2}/s was considered fast transient variation, while 1000 W/m

^{2}/s was considered slow variation. Each of the algorithms was adapted to obtain maximum power extraction, and thus, an accurate comparison of the results.

^{2}; at 0.133 s, this value increases to 1000 W/m

^{2}, and at 0.266 s, another transition occurs, with a final value of 600 W/m

^{2}. The step variation simulation results of each algorithm are presented in Figure 13 and Figure 14, which contain the HIL results. These results were obtained using a Tektronix DPO 2014B oscilloscope.

^{2}; at 0.1 s, the value gradually increases to 1000 W/m

^{2}, stabilizes for 0.1 s, and then decreases to 300 W/m

^{2}between 0.3 and 0.4 s. The simulation results for this scenario are presented in Figure 15 and Figure 16, which show the HIL results.

^{2}for 0.1 s; then, the irradiance increases from 600 W/m

^{2}to 700 W/m

^{2}for 0.1 s. After this increase, the value remains unchanged for 0.1 s, and finally decreases to 600 W/m

^{2}.

#### 4.3. Required Hardware Resources

## 5. Discussion

## 6. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

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**Figure 2.**Current–voltage and power–voltage characteristic curves of PV A10J-M60-240: (

**a**) different irradiances at 25 °C; and (

**b**) different temperatures at 1000 W/m

^{2}.

**Figure 10.**MPPT HIL test setup. 1—Oscilloscope; 2—DAC7558EVM; 3—expansion board XM105; 4—FPGA Xilinx ZC706; 5—computer; 6—router.

**Figure 12.**Irradiance level applied to PV to simulate different scenarios: (

**a**) steady state; (

**b**) step variation; (

**c**) fast variation; and (

**d**) slow variation.

**Table 1.**Fuzzy rule table based on [5].

Fuzzy Rule | S(k) | |||||
---|---|---|---|---|---|---|

NB | NS | ZE | PS | PB | ||

ΔS(k) | NB | ZE | PB | PS | ZE | NB |

NS | PB | PS | ZE | ZE | NB | |

ZE | PB | PS | ZE | NS | NB | |

PS | PB | ZE | ZE | NS | NB | |

PB | PB | ZE | NS | NB | ZE |

Parameter | Value |
---|---|

V_{oc} (PV open circuit voltage) | 36.84 V |

I_{sc} (PV short circuit current) | 8.32 A |

V_{MPP} (PV MPP voltage) | 30.72 V |

I_{MPP} (PV MPP current) | 7.83 A |

P_{MPP} (PV MPP power) | 240.54 W |

L (inductor) | 300 µH |

C_{in} (input capacitor) | 150 µF |

C_{out} (output capacitor) | 150 µF |

f_{sw} (switching frequency) | 50 kHz |

V_{mg} (microgrid voltage) | 48 V |

R_{mg} (microgrid resistance) | 50 mΩ |

Algorithm | Step Variation | Fast Variation | Slow Variation | Steady State * |
---|---|---|---|---|

P&O | 97.03% | 97.14% | 95.58% | 99.98% |

INC | 97.85% | 98.01% | 96.96% | 99.91% |

FL | 99.03% | 99.08% | 99.20% | 99.87% |

ANN (G, T) | 99.94% | 100.00% | 99.96% | 100.00% |

IC-INC | 99.95% | 99.67% | 99.89% | 99.97% |

ANN (IC-INC) | 99.67% | 98.50% | 99.86% | 99.94% |

Algorithm | Step Variation | Fast Variation | Slow Variation | Steady State |
---|---|---|---|---|

P&O | 98.36% | 98.94% | 99.11% | 99.04% |

INC | 99.21% | 98.98% | 99.04% | 99.17% |

FL | 99.14% | 98.81% | 98.64% | 99.12% |

ANN (G, T) | 97.88% | 98.55% | 99.06% | 97.95% |

IC-INC | 98.54% | 98.92% | 99.10% | 99.23% |

ANN (IC-INC) | 97.86% | 98.66% | 99.36% | 99.12% |

Algorithm | LUTs (218,600) | F7 Muxes (109,300) | F8 Muxes (54,650) | DSPs (900) |
---|---|---|---|---|

P&O | 1.08% | 0.01% | 0.00% | 0.22% |

INC | 2.48% | 0.01% | 0.00% | 0.00% |

FL | 5.92% | 2.02% | 1.67% | 0.89% |

ANN (G, T) | 28.38% | 0.08% | 0.02% | 11.78% |

IC-INC | 2.53% | 0.00% | 0.00% | 0.44% |

ANN (IC-INC) | 63.76% | 0.08% | 0.02% | 30.67% |

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**MDPI and ACS Style**

André, S.; Silva, F.; Pinto, S.; Miguens, P.
Novel Incremental Conductance Feedback Method with Integral Compensator for Maximum Power Point Tracking: A Comparison Using Hardware in the Loop. *Appl. Sci.* **2023**, *13*, 4082.
https://doi.org/10.3390/app13074082

**AMA Style**

André S, Silva F, Pinto S, Miguens P.
Novel Incremental Conductance Feedback Method with Integral Compensator for Maximum Power Point Tracking: A Comparison Using Hardware in the Loop. *Applied Sciences*. 2023; 13(7):4082.
https://doi.org/10.3390/app13074082

**Chicago/Turabian Style**

André, Sérgio, Fernando Silva, Sónia Pinto, and Pedro Miguens.
2023. "Novel Incremental Conductance Feedback Method with Integral Compensator for Maximum Power Point Tracking: A Comparison Using Hardware in the Loop" *Applied Sciences* 13, no. 7: 4082.
https://doi.org/10.3390/app13074082