# Accelerated Particle Swarm Optimization for Photovoltaic Maximum Power Point Tracking under Partial Shading Conditions

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Overview of Particle Swarm Optimization Algorithm

- Step 1:
- Initialize the particles randomly in the search space.
- Step 2:
- Evaluate the fitness value of each particle by sending the candidate solution to the objective function.
- Step 3:
- Update ${P}_{best}$ and ${G}_{best}$.
- Step 4:
- Update the position and velocity of each particle.
- Step 5:
- Re-initialize the PSO algorithm unless the constrain is met. In other words, the algorithm stops when the ${G}_{best}$ is founded.

_{1}= 0.2, X

_{2}=0.5, X

_{3}= 0.8. The output PV power is selected as the fitness function value to be maximized.

_{2}is served as ${G}_{best}$ because it has the highest PV output power (as shown in Figure 3a). The velocity $\Delta {\mathrm{d}}_{i}^{k+1}$ and position ${d}_{i}^{k+1}$ of each particle is updated accordingly after the first iteration.

_{2}is still the best particle. It is worth noting that as soon as the particles move to ${G}_{best}$, the velocity becomes smaller. Since all duty cycles achieve higher PV output power, the velocity direction of these particles remains unchanged and moved to ${G}_{best}$. After several interactions, it can be observed that all particles reach global MPP (GMPP) after several iterations, as shown in Figure 3c.

## 3. Proposed Accelerated PSO Algorithm

- Step 1
- (Parameter Selection): The number of particles is three. A complete optimization analysis has been done in [24], and it claimed that three particles deliver the best performance.
- Step 2
- (APSO Initialization): In the proposed APSO algorithm, the particles are placed on fixed positions. The first particle is set as 10% of the PV open circuit voltage (${V}_{oc}$), the third particle is set as 90% of ${V}_{oc}$. The first and third particles defined the PSO search space. The second particle is randomly set between 10% and 90% of ${V}_{oc}$.
- Step 3
- (Fitness Evaluation): The purpose of the PSO-based MPPT method is to maximize the PV output power. PV voltage and current are measured to compute the PV output power as the fitness value for evaluation.
- Step 4
- (Update the Global Value): The particle which has the best fitness value is selected as the ${G}_{best}$. In conventional PSO-based MPPT algorithms, ${G}_{best}$ is usually fixed. In this proposed APSO method, P&O MPPT algorithm is used to directly perturb the ${G}_{best}$ to accelerate the global MPP searching, so that ${G}_{best}$ will be moved towards a higher fitness value. In conventional PSO-based MPPT algorithms, the velocity of the particle is reducing when the particle is moving toward the ${G}_{best}$. In this proposed APSO method, ${G}_{best}$ can move to a higher fitness value via P&O algorithm, and simultaneously attracts the remaining particle more rapidly to converge toward it. Therefore, the convergence time could be decreased.

- Step 5
- (Update the Velocity and Position of Each Particle): Once all the particles are assessed, the position and velocity of each particle need to be updated.
- Step 6
- (Convergence Determination): Two convergence criteria will be examined in this step. If the particle’s velocity becomes lower than a set value or if the maximum iteration number is reached, the algorithm computation will be stopped, and the global MPP is found.
- Step 7
- (Re-initialization): The global MPP position frequently changes with the environmental conditions. This requires the APSO algorithm to be reinitialized and search for the new global MPP. In this research, Equation (10) is used to identify the environmental conditions changes and reinitialize the APSO algorithm.$$\frac{{P}_{PV,\text{}new}-{P}_{PV,\text{}last}}{{P}_{PV,\text{}last}}\Delta P(\%)$$

_{2}= 0.60. During the first iteration, particles X

_{1}and X

_{3}followed the optimal particle position X

_{2}to arrive at their new location for the next iteration. X

_{2}represents the particle with the highest fitness value (${G}_{best}$). P&O algorithm is employed to move X

_{2}toward the global MPP. By end of this iteration, X

_{2}value is also updated, as shown in Figure 5b. The particles position and velocity of the three particles are updated via more iterations.

_{2}= 0.52) as shown in Figure 5c. This process continues until particles X

_{1}and X

_{3}reach the global MPP as illustrated in Figure 5d. The proposed APSO algorithm can move the operating point to the global MPP quicker and has faster convergence speed compared to the conventional PSO algorithm. If a large change of environmental condition is detected, the particles (duty cycles) will be re-initialized, and the APSO algorithm is run again to search for the new global MPP.

## 4. Experimental Results

#### 4.1. Experimental Setup Configuration

#### 4.2. Setting the Parameter Values of the Particle Swarm Optimization Algorithm

#### 4.3. Case Studies

_{m}has a typical uncertainty ΔV

_{m}of ±0.3 V, and the current measurement I

_{m}has a typical uncertainty ΔI

_{m}of ±10 mA. The power measurement uncertainty ΔP

_{m}can be obtained by:

#### 4.4. Test under Partial Shading Variations

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 1.**Photovoltaic (PV) output power curves of three different partial shading patterns. (

**a**) partial shading pattern 1; (

**b**) partial shading pattern 2; and (

**c**) partial shading pattern 3.

**Figure 3.**How a standard PSO algorithm scan the P–V curve of a photovoltaic (PV) module to find global maximum power point (GMPP).

**Figure 5.**(

**a**) Particles are initialized on a PV curve. (

**b**) New position of particles after first iteration. (

**c**) Particle X

_{2}reaches GMPP by the end of second iteration. (

**d**) All particles are approaching the GMPP.

**Figure 9.**Convergence characteristics of (

**a**) Proposed APSO, (

**b**) PSO, (

**c**) Simplified PSO in [36], and (

**d**) P&O under Scenario 1.

**Figure 11.**Convergence characteristics of (

**a**) Proposed APSO, (

**b**) PSO, (

**c**) Simplified PSO in [36], and (

**d**) P&O under Scenario 2.

**Figure 13.**Convergence characteristics of (

**a**) Proposed APSO, (

**b**) PSO, (

**c**) Simplified PSO in [36], and (

**d**) P&O under Scenario 3.

**Figure 14.**Convergence Characteristics of (

**a**) Proposed PSO, (

**b**) PSO, (

**c**) Simplified PSO in [36], and (

**d**) P&O under changing partial shading conditions.

Parameter | P&O | PSO | Proposed APSO |
---|---|---|---|

Number of Particles | $\mathit{d}$ = 0.2 | 3 | 3 |

w | $\Delta \mathit{d}$ = 0.01 | 0.4 | --- |

${\mathit{c}}_{1}$ | --- | 1.2 | --- |

${\mathit{c}}_{2}$ | --- | 1.4 | --- |

$\beta $ | --- | --- | 0.1–0.7 |

Sampling time | 0.12 s | 0.12 s | 0.12 s |

**Table 2.**Summary of Comparison results of APSO, PSO, simplified PSO in [36], and P&O methods in terms of power tracked, efficiency, and tracking time.

Shading Scenario | Method | V_{mpp} (V) | I_{mpp} (A) | P_{mpp} (W) | Rated Power (W) | Efficiency (%) | Tracking Time (s) |
---|---|---|---|---|---|---|---|

Scenario (1) | APSO | 23.54 | 1.72 | 40.56 | 40.76 | 99 | 2.4 |

PSO | 22.55 | 1.75 | 39.44 | 97 | 4.6 | ||

PSO [36] | 23.45 | 1.72 | 40.37 | 99 | 3.2 | ||

P&O | 30.89 | 1.16 | 35.87 | 76 | 1.1 | ||

Scenario (2) | APSO | 31.54 | 2.32 | 73.33 | 73.62 | 99 | 1.9 |

PSO | 31.54 | 2.3 | 73.33 | 99 | 3 | ||

PSO [36] | 31.44 | 2.23 | 70.31 | 96 | 2.8 | ||

P&O | 32.24 | 2.233 | 72.00 | 98 | 1.9 | ||

Scenario (3) | APSO | 22.01 | 3.47 | 76.51 | 76.53 | 99 | 2.3 |

PSO | 22.07 | 3.27 | 72.17 | 94 | 4.2 | ||

PSO [36] | 21.95 | 3.48 | 76.39 | 99 | 3.2 | ||

P&O | 31.31 | 1.41 | 44.1 | 58 | 1.2 |

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## Share and Cite

**MDPI and ACS Style**

Alshareef, M.; Lin, Z.; Ma, M.; Cao, W.
Accelerated Particle Swarm Optimization for Photovoltaic Maximum Power Point Tracking under Partial Shading Conditions. *Energies* **2019**, *12*, 623.
https://doi.org/10.3390/en12040623

**AMA Style**

Alshareef M, Lin Z, Ma M, Cao W.
Accelerated Particle Swarm Optimization for Photovoltaic Maximum Power Point Tracking under Partial Shading Conditions. *Energies*. 2019; 12(4):623.
https://doi.org/10.3390/en12040623

**Chicago/Turabian Style**

Alshareef, Muhannad, Zhengyu Lin, Mingyao Ma, and Wenping Cao.
2019. "Accelerated Particle Swarm Optimization for Photovoltaic Maximum Power Point Tracking under Partial Shading Conditions" *Energies* 12, no. 4: 623.
https://doi.org/10.3390/en12040623