# Impact of PSO Reinitialization on the Accuracy of Dynamic Global Maximum Power Detection of Variant Partially Shaded PV Systems

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## Abstract

**:**

## 1. Introduction

_{best}) is less than the minimum duty ratio change, ΔD

_{min}; and second, the variation between the current and global power is greater than (P

_{GMP}* ΔP); where P

_{GMP}is the global maximum power and ΔP is the power change. These detection methodologies [9,12,16,19,20,21,22,23,24,25] do not guarantee that the SP has changed. It may happen due to load or/and normal radiation changes even without changes in SP. In addition, although the radiation may change, the searching region may not; hence, there is no need for PSO reinitialization, which may cause undesirable disturbances in the PV system.

## 2. Description of the Partially Shaded Photovoltaic System

^{2}) and temperature (°C). Three PV arrays with three different irradiances are used for representing the time-variant PSCs. As a result of PSCs, multiple maximum power peaks are generated for each shading pattern; here, the three maximum power points are one GMP and two LMPs; and the occurrence of the GMP at different places of the P–V curve is achieved under time-variant radiation or SPs. The variant irradiance will make the GMP change its position along with the voltage. Three different partial shading patterns are applied continuously with three different GMP positions and values (GMP locates 1st, GMP locates 2nd, GMP locates 3rd) as shown in Figure 2. Time-variant irradiances are used to generate GMPs at different positions to see the PSO response to follow the GMP if it changes its position with and without initialization (particle dispersion). As shown in Figure 1, Matlab/Simulink includes the PV energy system under variant partial shading; the improved PSO algorithm is in M-file. The improved PSO gets the PV voltage, current, and power at each duty cycle sent to the converter in Simulink.

## 3. Global Peak Extraction Using Particle Swarm Optimization Technique

_{i}

^{k}and v

_{i}

^{k}, respectively. The particle’s new position can be estimated as follows [10]:

_{i}

^{k}, the particle’s velocity v

_{i}

^{k}, the acceleration coefficients (c

_{1}and c

_{2}), the random numbers (r

_{1}, r

_{2}), and the personal and global best position (P

_{best i}and G

_{best}) as follows:

_{1}and r

_{2}) and retaining the accelerating factors, the velocity of the particle can be estimated as follows:

## 4. Proposed Particle Swarm Optimization Techniques

#### 4.1. State of the Art PSO Methodology without Reinitialization (Case-1)

- Step 1:
- Initialize the PSO parameters (ω, c
_{1}, c_{2}, and c_{3}) and send the initial duty cycles sequentially to the partially shaded PV system (objective function) and gather the associated powers values. - Step 2:
- Update the particles’ position and velocity (${x}_{i}^{k+1}$ and ${v}_{i}^{k+1}$) using Equations (1) and (5), respectively, then obtain the new duty cycles values of the converter.
- Step 3:
- Send new duty cycles (particles’ position) to the partially shaded PV system and gather the associated powers values.
- Step 4:
- Assess P
_{best,i}, G_{best}and their related particles’ positions, then; go back to Step 2.

#### 4.2. Improved PSO Reinitialization upon Predefined Time (Case-2)

- Step 1:
- Initialize the improved PSO parameters (ω, c
_{1}, c_{2}, and c_{3}), send the initial duty cycles sequentially to the partially shaded PV system (objective function), and gather the associated powers values. - Step 2:
- Step 2: Update the particles’ position and velocity (${x}_{i}^{k+1}$ and ${v}_{i}^{k+1}$) using Equations (1) and (5), respectively, then obtain the new duty cycles values of the converter.
- Step 3:
- Send the new duty cycles (particles’ position) to the partially shaded PV system and gather the associated powers values.
- Step 4:
- Assess P
_{best,i}, G_{best}and their related particle’s position, then check if the time is less than PDT (iteration < 100), go back to Step 2 otherwise go to Step 1.

#### 4.3. Improved PSO Reinitialization upon Shading Pattern Change (Case-3)

- Step 1:
- Initialize the improved PSO parameters (ω, c
_{1}, c_{2}, and c_{3}), send the initial duty cycles sequentially to the partially shaded PV system (objective function), and gather the associated powers values. - Step 2:
- Update the particles’ position and velocity (${x}_{i}^{k+1}$ and ${v}_{i}^{k+1}$) using Equations (1) and (5), respectively, then obtain the new duty cycles values of the DC–DC converter.
- Step 3:
- Send the new duty cycles (particles’ position) to the partially shaded PV system and gather the associated powers values.
- Step 4:
- Assess P
_{best,i}, G_{best}and their related particle’s position, then check if the SP of the PV system is not changed, go again to Step 2 otherwise go to Step 1.

_{new}and Ir

_{old}are the average irradiance for the new and previous iteration, respectively. ε is the irradiance change limit that has been assumed as 5%.

## 5. Simulation Results and Discussion

#### 5.1. Conventional PSO without Reinitialization (Case-1)

- From 0–40 s: PSO searches for the first GMP in a certain searching area and succeeds in catching the first GMP power (54.6 kW) for SP1 as illustrated in Figure 5.
- From 40–80 s: The partial shading pattern changed to SP2; hence, the GMP value (92.8 kW) and position (2nd GMP peak) also changed. Nevertheless, PSO cannot catch the new GMP power and remains in the first GMP searching area and its G
_{best}(d = 0.785). Therefore, it tracks the nearest peak in the same region of the first GMP (LMP equals to 49.6 kW); however, the current GMP is 92.8 kW for SP2. The reason is that the PSO reinitialization is not executed upon the SP change. - From 80–120 s: In a similar manner, the partial shading pattern is changed (SP3); hence, the GMP value (128.8 kW) and position (3rd GMP peak) also changes. Nevertheless, PSO cannot catch the new GMP and remains in the first GMP searching area and its G
_{best}(d = 0.785). Therefore, it tracks the nearest peak at the same region of the first GMP (LMP equals to 54.8 kW); however, the current GMP is 128.8 kW for SP3. The reason is that the PSO reinitialization is not executed upon the SP change.

#### 5.2. Improved PSO Reinitialization Based on Predefined Time (Case-2)

- From 0–24 s: The improved PSO caught the first GMP power (54.6 kW and 124 V) for SP1 as presented in Figure 6.
- From 24–40 s: The improved PSO reinitialization is executed, but the partial shading pattern has not changed; therefore, the system works again after reinitialization at the same situation (54.6 kW and 124 V). This reinitialization methodology has unwanted reinitialization that may disturb the PV system. Therefore, the reinitialization methodology upon PDT is no better in partial shading conditions.
- From 40–48 s: The partial shading pattern changes to SP2; hence, the GMP value and position also changes, but the improved PSO will not catch it until improved PSO reinitialization is executed. It remains at the nearest peak in the same region of the first GMP (LMP equals to 49.6 kW) until the improved PSO initialization is executed. This reinitialization has a delayed response to follow the new GMP of the new SP. Therefore, the reinitialization methodology upon PDT is no better in partial shading conditions.
- From 48–72 s: The particles are dispersed at the beginning of this period and the particles will catch the new GMP power (92.8 kW and 257 V) at d = 0.43.
- From 72–80 s: The improved PSO is reinitialized at the beginning of this period, but the SP has not changed; hence, the system will go again to the previous GMP point (92.8 kW and 257 V). Unwanted reinitialization occurs, which may disturb the PV system. Therefore, the reinitialization methodology upon PDT is no better in partial shading conditions.
- From 80–96 s: The partial shading pattern changes (SP3); hence, the GMP value and position also changes, but the improved PSO will not catch it until the improved PSO reinitialization is executed. It remains at the nearest peak in the same region of the second GMP (LMP equals to 100 kW) until PSO reinitialization is executed. A delayed response occurs in order to follow the new GMP of the new SP. Therefore, the reinitialization methodology upon PDT is no better in partial shading conditions.
- From 96 to 120 s: The improved PSO is reinitialized at the beginning of this period and the particles find the new GMP (129 kW at 402 V) for SP3.

#### 5.3. Improved PSO Reinitialization Upon the SP Change (Case-3)

- From 0–40 s: Improved PSO has successfully caught the first GMP power (54.6 kW and 124 V) for SP1 as shown in Figure 7.
- From 40–80 s: The partial shading pattern changed to SP2, both the GMP value (92.8 kW) and its position also changed (2nd GMP peak). PSO reinitialization is executed upon the SP change at t = 40 s. Improved PSO succeeded in finding the second GMP peak (92.8 kW) efficiently and accurately as shown in Figure 7.
- From 80–120 s: In a similar manner, the partial shading pattern changed to SP3. Reinitialization is executed upon the partial shading pattern change at t = 80 s. The improved PSO succeeded in finding the third GMP peak (128.8 kW) efficiently and accurately, as shown in Figure 7. The performance efficiency for this PV system is 100%, which reflects the effective performance of improved PSO reinitialization upon the partial shading pattern change. This reinitialization methodology solved the two shortcomings of the previous reinitialization methodology (PDT); unwanted reinitialization and delayed response.

## 6. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Nomenclature

GMP | Global maximum power; |

PV | Photovoltaic; |

SP | Shading Pattern; |

PSO | Particle swarm optimization; |

PSC | Partial shading condition |

P_{best,i} | Personal best solution; |

G_{best} | Global best of P_{best,i}; |

x_{i}^{k} | Position vector; |

v_{i}^{k} | Velocity vector; |

ω | Inertia weight; |

c_{1} and c_{2} | Acceleration coefficients; |

r_{1}, r_{2} | Random numbers; |

MPPT | Maximum Power Point Tracker; |

FPA | Flower pollination algorithm; |

FA | Firefly algorithm; |

CSO | Cuckoo search optimization; |

ABC | Ant bee colony; |

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**Figure 3.**Improved Particle Swarm Optimization (PSO) reinitialization flowchart based on predefined time (PDT).

**Figure 5.**The PV output response under variant partial shading pattern based on PSO without reinitialization.

**Figure 6.**The PV output response under variant partial shading patterns based on improved PSO reinitialization upon PDT.

**Figure 7.**The PV output response under variant partial shading pattern based on improved PSO reinitialization upon the radiation change.

**Table 1.**Comparisons of the improved PSO using the two proposed methodologies with the conventional PSO.

SP No. Cases | SP#1 | SP#2 | SP#3 | |
---|---|---|---|---|

Irradiance (W/m^{2}) | (1000, 300, 200) | (800, 400, 900) | (1000,700, 900) | |

GMP value (kW) | 54.6 | 92.8 | 128.8 | |

GMP place | 1st | 2nd | 3rd | |

V_{PV} at GMP (V) | 124 | 257 | 402 | |

PSO without reinitialization | P_{PV} (kW) | 54.6 | 49.6 | 54.8 |

V_{PV} (V) | 124 | 124 | 124 | |

PSO Efficiency | 100% | 53% | 43% | |

Improved PSO reinitialization upon PDT | P_{PV} (kW) | 54.6 | 49.6–92.8 | 54.8–128.8 |

V_{PV} (V) | 124 | 124–257 | 257–402 | |

Improved PSO Efficiency | 100% | 53% → 100% | 43% → 100% | |

Improved PSO reinitialization upon SP change | P_{PV} (kW) | 54.6 | 92.8 | 128.8 |

V_{PV} (V) | 124 | 257 | 402 | |

Improved PSO Efficiency | 100% | 100% | 100% |

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## Share and Cite

**MDPI and ACS Style**

Eltamaly, A.M.; M. H. Farh, H.; S. Al Saud, M.
Impact of PSO Reinitialization on the Accuracy of Dynamic Global Maximum Power Detection of Variant Partially Shaded PV Systems. *Sustainability* **2019**, *11*, 2091.
https://doi.org/10.3390/su11072091

**AMA Style**

Eltamaly AM, M. H. Farh H, S. Al Saud M.
Impact of PSO Reinitialization on the Accuracy of Dynamic Global Maximum Power Detection of Variant Partially Shaded PV Systems. *Sustainability*. 2019; 11(7):2091.
https://doi.org/10.3390/su11072091

**Chicago/Turabian Style**

Eltamaly, Ali M., Hassan M. H. Farh, and Mamdooh S. Al Saud.
2019. "Impact of PSO Reinitialization on the Accuracy of Dynamic Global Maximum Power Detection of Variant Partially Shaded PV Systems" *Sustainability* 11, no. 7: 2091.
https://doi.org/10.3390/su11072091