# A New Strategy for PI Tuning in Photovoltaic Irrigation Systems Based on Simulation of System Voltage Fluctuations Due to Passing Clouds

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## Abstract

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## 1. Introduction

## 2. Materials and Methods

- Data collection of the PVIS system operation under different passing clouds.
- Data analysis to identify clouds.
- Method for simulation using the feedforward input.

- The definition of the most suitable feedforward signal for the PID tuning based on the relationship between the system voltage, the derivative of irradiance and the output frequency.
- Development of the tuning process for both, stable operation and start-up of the PVIS. This section has been structured accordingly.

#### 2.1. Laboratory Experimentation System

- PV array. $P=170$${W}_{p}$; ${V}_{mp}=277.1$V.
- Variable frequency drive (VFD). Three-phase 200 V; 0.75 kW.
- A monitoring and control system using:
- -
- Arduino based PLC (IndustrialShields).
- -
- MQTT for communication protocol.
- -
- Voltage, current, irradiance and temperature sensor. Frequency can be obtained from VFD.

- Oscilloscope and signal generator.

#### 2.2. Methodology to Simulate System Voltage Drops Caused by Passing Clouds

- -
- Step 1: Data collection

- -
- Step 2: Data analysis to identify clouds

- Cloud recognition starts when the value of the calculated derivative is below the set threshold.
- Each of the derivative samples is analysed until its value is close to 0. If irradiance is stable, the cloud has finished.
- Advanced cloud filtering is available. For example, it can be configured to only display clouds that cause an irradiance decrease of a given value or given duration.

- -
- Step 3: Simulation of system voltage drop caused by clouds using the VFD feedforward input

- Get maximum value of the irradiance curve corresponding to a passing cloud.
- Subtract each irradiance sample to the maximum obtained in the first step.
- Divide by the maximum of the curve to normalize and get 1 as maximum.

#### 2.3. PID Tuning Method

#### 2.3.1. Most Suitable Feedforward Signal for PID Tuning Based on the Relationship between System Voltage, Derivative of Irradiance and Output Frequency

#### 2.3.2. Tuning Process

- ${K}_{p}$ smaller than optimal.
- ${T}_{i}$ larger than optimal.

- ${K}_{p}$ modifies the system voltage waveform. The larger ${K}_{p}$ is, the smoother the step of the squared signal of the system voltage. If it is too small, oscillation occurs, which can be dangerous for the PVIS. This is true when using small ${T}_{i}$, which is what happens in this type of system.
- ${T}_{i}$ modifies the total amplitude of the system voltage signal. Low ${T}_{i}$ values result in low amplitudes, but making it too small results in an unstable and oscillating system.

- A triangular feedforward signal with a certain amplitude is chosen. At the beginning it should be very small but enough to produce a noticeable disturbance. It is important to note that it is not sufficient to introduce only a single disturbance. A train of at least two pulses of the triangular signal shall be introduced.A train of changes in the slope of the signal will produce more noticeable disturbances that would not occur with a single pulse.
- The value of ${K}_{p}$ is progressively increased and the triangular pulse train is reintroduced until the voltage response is as close as possible to a square wave. If a waveform as close to a square wave as possible is not achieved, the value of ${T}_{i}$ should be slightly reduced. See details in Section 3.2.1.
- The ${T}_{i}$ is gradually lowered until a small amplitude is reached in the train of square pulses of the system voltage, but without causing the system to oscillate and become unstable.
- The amplitude of the triangular signal is slightly increased so that the disturbance in the system voltage is greater. Repeat steps 2 and 3 again adjusting the parameters until the triangular signal amplitude is close to the maximum of the input feedforward (50 Hz) and is supported by the system.

#### 2.3.3. Tuning for Start-Up

- Program an adaptive PI. This means that the PI parameters at start-up and in normal operation will be different.
- Compromise to obtain an acceptable start and behaviour in all situations.

- ${K}_{p}/3$
- ${T}_{i}\xb73$

## 3. Results

#### 3.1. Results Related with the Simulation of System Voltage Drop Caused by Passing Clouds

#### 3.2. Results Related with the New PI Tuning Method

#### 3.2.1. Tuning for Normal Operation

#### 3.2.2. Tuning for Start-Up

#### 3.2.3. Influence of PI Tuning on the System Voltage Drop Simulation

#### 3.3. About the Generalization of the Results

## 4. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Abbreviations

VFD | Variable Frequency Drive |

V | Voltage |

PV | Photovoltaic |

PVIS | Photovoltaic Irrigation Systems |

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**Figure 2.**Cloud 1 (50.59% irradiance drop): irradiance fluctuation and corresponding system voltage disturbance.

**Figure 3.**Cloud 2 (59.41% irradiance drop): irradiance fluctuation and corresponding system voltage disturbance.

**Figure 7.**Feedforward signal, equivalent to the normalized and inverted irradiance, used to simulate the system voltage drop corresponding to Cloud 2.

**Figure 11.**System voltage disturbances produced by different amplitudes of the feedforward signal for Cloud 1.

**Figure 12.**System voltage disturbances produced by different amplitudes of the feedforward signal for Cloud 2.

**Figure 15.**System voltage disturbance with a triangular feedforward signal, different ${K}_{p}$ and ${T}_{i}=0.1$.

**Figure 16.**System voltage disturbance with a triangular feedforward signal, different ${K}_{p}$ and ${T}_{i}=0.2$.

**Figure 17.**System voltage disturbance with a triangular feedforward signal, different ${T}_{i}$ and ${K}_{p}=3$.

DC Voltage Drop (V) | ||
---|---|---|

Feedforward Amplitude (V) | Cloud 1 | Cloud 2 |

1 | 7.19 | 8.73 |

2 | 14.14 | 17.63 |

3 | 20.84 | 27.63 |

4 | 27.05 | 34.82 |

5 | 34.56 | 44.1 |

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**MDPI and ACS Style**

Guillén-Arenas, F.J.; Fernández-Ramos, J.; Narvarte, L. A New Strategy for PI Tuning in Photovoltaic Irrigation Systems Based on Simulation of System Voltage Fluctuations Due to Passing Clouds. *Energies* **2022**, *15*, 7191.
https://doi.org/10.3390/en15197191

**AMA Style**

Guillén-Arenas FJ, Fernández-Ramos J, Narvarte L. A New Strategy for PI Tuning in Photovoltaic Irrigation Systems Based on Simulation of System Voltage Fluctuations Due to Passing Clouds. *Energies*. 2022; 15(19):7191.
https://doi.org/10.3390/en15197191

**Chicago/Turabian Style**

Guillén-Arenas, Francisco Jesús, José Fernández-Ramos, and Luis Narvarte. 2022. "A New Strategy for PI Tuning in Photovoltaic Irrigation Systems Based on Simulation of System Voltage Fluctuations Due to Passing Clouds" *Energies* 15, no. 19: 7191.
https://doi.org/10.3390/en15197191