# A Novel Plant Propagation-Based Cascaded Fractional Order PI Controller for Optimal Operation of Grid-Connected Single-Stage Three-Phase Solar Photovoltaic System

^{*}

## Abstract

**:**

## 1. Introduction

## 2. System Modeling

#### 2.1. PV Panel

#### 2.2. Perturbation and Observation (P&O)-Based MPPT

#### 2.3. Outer Voltage Control Loop and Inner Current Control Loop

## 3. Objective Function

#### 3.1. Optimization Process

#### 3.2. Particle Swarm Optimization

Algorithm 1. PSO |

1: Initialize X = Particle/Solution and v = Velocity |

2: while gen < max_gen |

3: for each particle x in X do |

4: fx = f(x) |

5: if fx is better than f(xBest) |

6: xBest = x; |

7: end |

8: gBest = best x in X |

9: for each particle x in X do |

10: update velocity and particle position using Equations (11) and (12) |

11: end for |

12: end while |

#### 3.3. Elephant Herding Optimization

Algorithm 2. EHO |

1: Initialize X=Particle/Solution |

2: while gen < max_gen |

3: Sort all the elephants according to the fitness |

4: Implement Clan updating operator by Equations (13) and (14) |

5: Implement Separating operator using Equation (15) |

6: Evaluate the population by updated positions |

7: gen = gen + 1; |

8: end while |

#### 3.4. Plant Propagation Algorithm

Algorithm 3. PPA |

1: Initialize X = Particle/Solution |

2: while gen < max_gen |

3: evaluate the fitness value of solutions |

4: for j = 1 to M |

5: evaluate normalized fitness using Equation (16) |

6: evaluate the number of new solutions generated by Equation (17) |

7: for i = 1 to N |

8: evaluate the length of the offspring by Equation (18) |

9: end for |

10: for r = 1 to ${\mu}_{j}$ |

11: for i = 1 to N |

12: evaluate the decision variable ith of new solution rth generated by Equation (19) |

13: end for |

14: end for |

15: end for |

16: Reform the new population with M best solutions |

17: end while |

## 4. Experimental Setup and Simulation Results

^{2}and a fixed temperature of 25 °C. In Figure 11b, unlike Figure 11a,c, there are different individual reference values for each of the optimization algorithms. This is because the reference value for the d-axis current controller comes from the output of the DC link voltage controller. As responses from different optimization techniques provide different outputs from the DC link voltage controller, the reference value also changes for the d-axis current controller.

#### 4.1. Index Comparison

#### 4.2. Boxplot Analysis for Global Optimization Analysis

## 5. Plant Propagation Algorithm-Based Controller Performance Analysis

#### 5.1. Power Quality Analysis Through Total Harmonic Distortion (THD) Analysis

#### 5.2. Performance under Varied Conditions

^{2}, then suddenly changed to 800 W/m

^{2}at 3 s, followed by 600, 700, and 400 W/m

^{2}at 4, 5, and 6 s respectively. The temperature was fixed at 25 °C, although it can also be varied. The corresponding reference and simulated power outputs can be seen in Figure 15c. Reference reactive power was also varied during this period in such a way that it does not violate the $Q\le \sqrt{{S}^{2}-{P}^{2}}$ condition. The DC link voltage controller was found to track the reference value very efficiently.

## 6. Conclusions and Future Work

## Author Contributions

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Single-stage three-phase grid-connected photovoltaic (PV) system: (

**a**) overall system; (

**b**) inside inverter control block.

**Figure 8.**Simulink model for real-time machine-in-loop (MIL) simulation in OPAL-RT: (

**a**) RTLAB-based Simulink interface; (

**b**) sc_user_interface block; (

**c**) sm_computation block.

**Figure 10.**Gain parameters’ trajectory with respect to generation: (

**a**) Kp gain of DC link voltage controller; (

**b**) Ki gain of DC link voltage controller; (

**c**) Kp gain of d- and q-axis current controller; (

**d**) Ki gain of d- and q-axis current controller; (

**e**) $\lambda $ of DC link voltage controller; (

**f**) $\lambda $ of current controller.

**Figure 11.**Controller time response. (

**a**) DC link voltage controller; (

**b**) d-axis current controller; (

**c**) q-axis current/reactive power controller.

**Figure 13.**Box plot for the objective function of the final generation population for every optimization technique.

Parameters | Values | Parameters | Values |
---|---|---|---|

Plant Capacity | 3026 kVA | Filter Resistance | 0.0015 pu |

Grid Voltage | 4.16 kV (${V}_{LL},rms$) | Filter Inductance | 0.15 pu |

Frequency | 60 Hz | Filter Capacitance | 0.1 pu |

DC Link Capacitance | 0.0720 F | Transformer Resistance | 0.0012 pu |

DC Link Voltage | 1450 Vdc | Transformer Inductance | 0.03 pu |

Each Unit Capacity | 213.15 W | Switching Frequency | 1980 Hz |

No. of Series Units | 50 | Sampling Time | 50 µs |

No. of Parallel Units | 213 |

Parameter | ${\mathit{K}}_{\mathit{p}\mathit{v}}$ | ${\mathit{K}}_{\mathit{i}\mathit{v}}$ | ${\mathbf{\lambda}}_{\mathit{v}}$ | ${\mathit{K}}_{\mathit{p}\mathit{I}}$ | ${\mathit{K}}_{\mathit{i}\mathit{I}}$ | ${\mathbf{\lambda}}_{\mathit{I}}$ |
---|---|---|---|---|---|---|

Max value | 0.8 | 40 | 1.5 | 4 | 400 | 1.5 |

Min value | 0.2 | 10 | 0.75 | 1 | 100 | 0.75 |

Algorithm | Parameter | Values |
---|---|---|

PSO | ${C}_{1},{C}_{2},w$ | 1.5, 1.5, 0.9 |

EHO | $\alpha ,\text{}\beta $ | 0.5, 0.5 |

PPA | ${\mu}_{max}$ | Population number/5 |

Controller | DC Link Voltage Controller | Current Controller | ||||
---|---|---|---|---|---|---|

Parameter | Kp | Ki | $\mathbf{\lambda}$ | Kp | Ki | $\mathbf{\lambda}$ |

PSO | 1.0054 | 100 | - | 0.6820 | 40 | - |

EHO | 1.5398 | 169.8523 | 0.9707 | 0.6498 | 18.9024 | 0.9394 |

PPA | 1.3858 | 100 | 0.8431 | 0.6654 | 17.5034 | 0.9757 |

Index | PSO | EHO | PPA |
---|---|---|---|

Objective Function | 0.325094 | 0.321471 | 0.2918 |

DC link controller Settling time (sec) | 0.1250 | 0.0900 | 0.1270 |

Id controller settling time (sec) | 0.1490 | 0.1060 | 0.0720 |

Iq/Q controller settling time (sec) | 0.1030 | 0.1550 | 0.1670 |

DC link controller Peak Overshoot (%) | 18.9178 | 17.9912 | 17.9831 |

Id controller peak overshoot (%) | 4.7317 | 5.0402 | 1.580398 |

Iq/Q Controller peak overshoot (%) | 89.1056 | 91.9191 | 96.4454 |

Convergence Speed (iteration) | 21 | 18 | 13 |

Parameters | ${\mathit{R}}_{\mathit{g}}$ and ${\mathit{L}}_{\mathit{g}}$ | |||
---|---|---|---|---|

% Changes of the Nominal Values | −10% | −5% | +5% | +10% |

Objective function values | 0.3046 | 0.2969 | 0.2850 | 0.3121 |

© 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/).

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**MDPI and ACS Style**

Zamee, M.A.; Won, D.
A Novel Plant Propagation-Based Cascaded Fractional Order PI Controller for Optimal Operation of Grid-Connected Single-Stage Three-Phase Solar Photovoltaic System. *Appl. Sci.* **2019**, *9*, 4269.
https://doi.org/10.3390/app9204269

**AMA Style**

Zamee MA, Won D.
A Novel Plant Propagation-Based Cascaded Fractional Order PI Controller for Optimal Operation of Grid-Connected Single-Stage Three-Phase Solar Photovoltaic System. *Applied Sciences*. 2019; 9(20):4269.
https://doi.org/10.3390/app9204269

**Chicago/Turabian Style**

Zamee, Muhammad Ahsan, and Dongjun Won.
2019. "A Novel Plant Propagation-Based Cascaded Fractional Order PI Controller for Optimal Operation of Grid-Connected Single-Stage Three-Phase Solar Photovoltaic System" *Applied Sciences* 9, no. 20: 4269.
https://doi.org/10.3390/app9204269