This paper develops a real-time PV arrays maximum power harvesting scheme under partial shading condition (PSC) by reconfiguring PV arrays using Aquila optimizer (AO). AO is based on the natural behaviors of Aquila in capturing prey, which can choose the best hunting mechanism ingeniously and quickly by balancing the local exploitation and global exploration via four hunting methods of Aquila: choosing the searching area through high soar with the vertical stoop, exploring in different searching spaces through contour flight with quick glide attack, exploiting in convergence searching space through low flight with slow attack, and swooping through walk and grabbing prey. In general, PV arrays reconfiguration is a problem of discrete optimization, thus a series of discrete operations are adopted in AO to enhance its optimization performance. Simulation results based on 10 cases under PSCs show that the mismatched power loss obtained by AO is the smallest compared with genetic algorithm, particle swarm optimization, ant colony algorithm, grasshopper optimization algorithm, and butterfly optimization algorithm, which reduced by 4.34% against butterfly optimization algorithm.

Recently, excessive energy demand has caused severe environmental deterioration and rapid energy exhaustion such as coal, oil, and natural gas, which requires a profound energy transformation due to the energy crisis [

To solve these thorny obstacles caused by PSC, a wide range of solutions have been proposed such as installing bypass diodes in parallel on PV panel [

Nowadays, PV array reconfiguration has been envisaged as a highly competitive strategy to harvest maximum power output under different PSCs, which basic principle is to rearrange the shadows in the same column of PV arrays through physical relocation (PR) [

In recent years, an optimal PV array reconfiguration (OAR) via various meta-inspiration algorithms is proposed, such as genetic algorithm (GA) [

Therefore, this work devises a new Aquila optimizer (AO) to extract the maximum power of PV power plants under PSC in real-time. For validation, a complete 15 × 15 TCT PV array reconfiguration model is implemented and tested in simulation. The main novelties of this work are outlined as follows:

● An AO based real-time maximum power harvesting strategy from PV arrays under PSC by reconfiguring PV arrays is proposed.

● Compared to the original AO [

● 10 cases under PSCs are designed to simulate possible shadows caused by clouds, trees, buildings, dust accumulation, bird droppings, and snow. Besides, the effectiveness of AO on PV array reconfiguration is tested under such 10 shadows.

The rest sections are organized as follows:

TCT-connected PV arrays are connected in parallel in each row, while these rows are connected in series. Because the voltages at both ends of each row are equal, the entire output voltage of the PV array is able to be modeled as

The law of Kirchhoff current indicates that the whole current flowing through each column of PV arrays can be described as

To evaluate the performance of OAR under PSC using AO, three indices (fill factor, mismatched power loss, and efficiency) are introduced, as follows:

^{2} and the operation temperature of 25°C.

AO is designed by simulating the natural behavior of Aquila in capturing prey. Aquila’s pointed hook-shaped beak and sharp claws can help them quickly catch all kinds of prey, such as hares, marmots, squirrels, and other ground animals. Most Aquila can choose the best hunting method ingeniously and quickly according to the situation.

Initial population of AO is randomly produced within the upper bound (

AO modeling is mainly realized by simulating Aquila’s behavior when they are hunting: (1) choosing the searching area through high soar with the vertical stoop, (2) exploring in different searching spaces through contour flight with quick glide attack, (3) exploiting in convergence searching area through low flight with slow attack, and (4) swooping through the walk and grabbing prey. AO can switch between exploration and exploitation based on the condition:

Aquila explores widely the searching area by high soar, as shown in

AO explores the area where the target prey appears to be ready for attacking, as described in

AO exploits the range where preys appear, and then approaches and attacks it, as shown the

Reconfiguring PV arrays is a problem of discrete optimization. To apply the excellent optimization performance of AO for solving this problem, a series of discrete designs are performed on AO, as follows:

Obviously, the method of population initialization shown in

_{pop} is the number of population.

At the process of PV array reconfiguration, each PV array only exchanges with another PV array in the same column. Thus, the optimization variables should satisfy the following constraints:

AO switches between exploration and exploitation according to the situation to choose the best hunting method ingeniously and quickly. To make the optimization method suitable for PV array reconfiguration, the sequence of solutions optimized by

Since the physical position of all arrays in TCT configuration is fixed, an OAR model via electrical switches is introduced to reconfigure the position of arrays. Firstly, a discrete design for AO is performed for OAR model to obtain the optimal electrical connection state. After that, the physical position of PV arrays is rearranged via electrical switches in conformity with the obtained electrical connection state.

The primary goal of PV power plant is to extract the maximum output power under PSC, and its objective function is expressed as

On the whole, the entire executive procedure of OAR based on AO is provided in

1: Input the real-time predictive weather conditions; |
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2: Initialize the parameters and population by |

3: Set |

4: Calculate the objective function |

5: |

6: Update the mean value of the current solution _{M}(t); |

7: Update the _{1},_{2}, Levy( |

8: |

9: |

10: Update the current solution _{1} using |

11: _{1}( |

12: _{1}( |

13: _{1}(_{best}( |

14: _{best}(_{1}( |

15: |

16: |

17: |

18: Update the current solution _{2} using |

19: _{2}( |

20: _{2}( |

21: _{2}(_{best}( |

22: _{best}(_{2}( |

23: |

24: |

25: |

26: |

27: |

28: Update the current solution _{3} using |

29: _{3}( |

30: _{3}( |

31: _{3}(_{best}( |

32: _{best}(_{3}( |

33: |

34: |

35: |

36: Update the current solution _{4} using |

37: _{4}( |

38: _{4}( |

39: _{4}(_{best}( |

40: _{best}(_{4}( |

41: |

42: |

43: |

44: |

45: |

46: Output the electrical connection state of OAR _{best}; |

47: Re-execute AO from step 1 to step 46 at the next case of shadow. |

In this work, AO is applied to a test PV power station under 10 cases of PSCs (see ^{2}, pale-yellow block is 900 W/m^{2}, light blue block is 800 W/m^{2} and others shown in ^{-3} s.

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

Number of strings in parallel | 10 |

Number of modules in series each string | 5 |

Number of cells each module | 60 |

Maximum output power each module | 224.98 W |

Open circuit voltage each module | 36.24 V |

Short-circuit current each module | 8.04 A |

Voltage of maximum power point each module | 30.24 V |

Current of maximum power point each module | 7.44 A |

_{max} and _{mean} are the maximum and mean values of output power in 30 independent runs. From _{max} and _{mean} (in bold). In addition, three evaluation indices (FF, _{mean} of 10 cases of PSCs. One can see clearly that AO can get the largest FF and

Case | GA | PSO | ACO | GOA | BOA | AO | |||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|

_{max} (MW) |
_{mean} |
_{max} (MW) |
_{mean} (MW) |
_{max} (MW) |
_{mean} |
_{max} (MW) |
_{mean} |
_{max} (MW) |
_{mean} |
_{max} (MW) |
_{mean} |
||

1 | 45.56 | 45.56 | 45.56 | 45.56 | 45.56 | 45.56 | 45.56 | 45.56 | 45.56 | 45.56 | |||

2 | 35.10 | 34.65 | 35.43 | 34.92 | 35.44 | 35.00 | 35.43 | 34.82 | 35.10 | 34.63 | |||

3 | 38.13 | 37.21 | 38.13 | 37.67 | 38.13 | 37.59 | 37.80 | 37.65 | 38.13 | 37.19 | |||

4 | 37.12 | 36.68 | 37.12 | 36.40 | 37.12 | 36.78 | 36.78 | 36.41 | 37.12 | 36.38 | |||

5 | 39.48 | 38.53 | 39.48 | 39.45 | 39.48 | 39.48 | 39.82 | 39.42 | 39.48 | 38.51 | |||

6 | 39.82 | 39.41 | 39.82 | 39.50 | 40.16 | 39.61 | 39.82 | 39.47 | 39.82 | 39.39 | |||

7 | 34.42 | 32.88 | 34.42 | 33.23 | 34.42 | 33.88 | 34.42 | 33.34 | 34.42 | 32.85 | |||

8 | 36.78 | 35.70 | 36.78 | 36.22 | 36.78 | 36.30 | 37.12 | 36.26 | 36.78 | 35.65 | |||

9 | 26.66 | 25.62 | 26.66 | 26.38 | 26.66 | 26.54 | 26.66 | 26.38 | 26.66 | 25.57 | |||

10 | 36.45 | 35.33 | 36.45 | 35.75 | 36.79 | 35.84 | 36.45 | 35.84 | 36.45 | 35.31 | |||

FF (Total) | 0.5515 | 0.5569 | 0.5592 | 0.5570 | 0.5507 | 0.5599 | |||||||

MMloss (Total) (MW) | 144.635 | 141.125 | 139.625 | 141.055 | 145.165 | 139.125 | |||||||

71.43 | 72.12 | 72.42 | 72.13 | 71.32 | 72.52 |

The optimal solution of the 15 × 15 PV arrays reconfigured by AO is provided in ^{th} case of PSC is 28.08% higher than that without optimization, as described in ^{th} case of PSC. It can be seen that AO can quickly converge to a high-quality optimal solution.

An AO based OAR is proposed for real-time maximum power extraction under PSC of PV arrays in this work, which contributions are drawn as follows:

(1) AO contains a series of discrete operations during optimization to solve the discrete problem of PV array reconfiguration, which owns great potential to apply in other complex discrete optimization problems.

(2) This work comprehensively considers the impact of PSC caused by clouds, trees, buildings, dust accumulation, bird droppings, and snow for PV array and simulates the 10 cases of PSCs based on this impact to validate the application reliability of AO under various PSCs.

(3) A series of experiments based on 10 cases of PSCs are designed to validate the optimization performance of AO compared against five well-known algorithms (e.g., GA, PSO, ACO, GOA, and BOA). Simulation results indicate that the mismatched power loss obtained by AO is the smallest, which can be decreased by 4.34% against BOA. Furthermore, it can be seen that the number of multiple peaks caused by the various PSCs can be significantly reduced by AO.

Future studies will focus on the following aspects:

(1) Apply the proposed AO based OAR to larger-scale PV arrays.

(2) Apply discrete AO to solve other discrete optimization problems.

the entire output voltage of the PV array

the maximum voltage of array at the

the whole current flowing through each column of PV arrays

output current across the

the output power of the testing PV power plant at the

the number of sub-systems of the testing PV power plant

objective function

the electrical connection state of PV arrays at the

the

the mean value of current solutions at the

the highest-quality solution gained during the

the levy flight distribution function

the quality function used to balance the search methods

the solution vector of arrays at the

maximum output power of PV array under PSC

_{max}

maximum output power of the testing PV power plant with 30 runs

_{mean}

mean output power of the testing PV power plant with 30 runs

upper bound of search spaces

lower bound of search spaces

maximum iteration number

open-circuit voltage of PV array

short-circuit voltage of PV array

maximum output power of PV array under standard condition

index of row

index of column

index of iteration

fill factor

mismatched power loss

efficiency

ant colony algorithm

Aquila optimizer

butterfly optimization algorithm

genetic algorithm

grasshopper optimization algorithm

maximum power point tracking

optimal PV array reconfiguration

partial shading condition

particle swarm optimization

total-cross-tied