Parameter Extraction of Solar Photovoltaic Model Based on Nutcracker Optimization Algorithm
Abstract
:1. Introduction
- Demonstrate the suitability and effectiveness of NOA in the field of the parameter extraction of the PV model.
- Employ modern techniques to accurately identify the optimum parameters in the PV model.
- Conduct a comparative study on four MAs to enhance the precision of a specific diode model optimization.
- Analyze possible future trends in the area based on the test results.
2. Solar Cell Model
2.1. Photovoltaic (PV) Cell Models
2.2. Optimization of Photovoltaic (PV) Cell Model Parameters
3. NOA
3.1. Overview of NOA
3.2. Foraging and Storage Strategy
3.3. Cache Search and Recovery Strategy
3.4. Implementation of NOA
Algorithm 1: Pseudo-code of NOA. |
Input: population size N, the lower limits of variables , the upper limits of variables the current number of iteration t = 0, and the maximum number of iterations . |
Output: the best solution found. |
1. Initialize N nutcracker/solution using Equation (14); |
2. Evaluate each solution and find the one with the best fitness in the population |
3. = 1; //the current function evaluation// |
4. while () |
5. Generate random numbers and , between 0 and 1. |
6. If < //* Foraging and storage strategy*// |
7. is a random number between 0 and 1. |
8. for i = 1: N |
9. for j = 1: d |
10. if /*Exploration phase1*/ |
11. Updating using Equation (1) |
12. else /*Exploitation phase1*/ |
13. Updating using Equation (3) |
14. end if |
15. end for |
16. Update the current iteration by |
17. end for |
18. else //* Cache-search and recovery strategy *// |
19. Generate RP matrix using Equations (5)–(7). |
20. Generate a random number between 0 and 1. |
21. for i = 1: N |
22. if /*Exploration phase2*/ |
23. Updating using Equation (9). |
24. else /*Exploitation phase2*/ |
25. Updating using Equation (12). |
26. end if |
27. |
28. end for |
29. end while |
4. Experimental Analysis
5. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
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Model | Circuit Equations |
---|---|
SDM | |
DDM | |
TDM | |
PV |
Evaluation Index | Formula |
---|---|
RMSE | 1 |
Model | Parameter Optimization Functions |
---|---|
SDM | |
DDM | |
TDM |
Parameters | Description |
---|---|
The current position/current cache of nutcrackers in iteration t. | |
The jth position of the ith nutcracker in the current generation. | |
Vectors, including the upper and lower bound of the jth dimension in the optimization problem. | |
, | A number generated according to the Lévy flight. |
The jth dimension of the best solution obtained. | |
,, | Random real numbers in the range of [0, 1]. |
The mean of the jth dimensions of all solutions of the current population in the iteration t. | |
A new position in the storage area of the nutcrackers in current iteration t. | |
A factor that linearly decreased from 1 to 0. | |
A probability value that is linearly decreased from one to zero. | |
, | RPs (objects) of the cache position of the ith nutcracker in the current generation t. |
The angle-of-view of the nutcracker, chosen at random from [0, π]. | |
, | The current and maximum generations. |
A probability value that is equal to 0.2. | |
A random vector in the interval [0, 1]. |
NOA | PSO | FWA | WOA | ||
---|---|---|---|---|---|
SDM | AVG-RMSE | 0.018868 | 2.298162 | 1.679379 | 3.061984 |
MD | 0.000099 | 1.698016 | 1.698207 | 1.698016 | |
STD | 0.079632 | 1.658716 | 0.103535 | 2.336065 | |
DDM | AVG-RMSE | 0.488002 | 1.447042 | 1.267698 | 1.557119 |
MD | 0.024675 | 1.309913 | 1.310957 | 1.672228 | |
STD | 0.636135 | 0.244036 | 0.131228 | 0.236466 | |
TDM | AVG-RMSE | 0.003819 | 0.250803 | 0.378707 | 0.304575 |
MD | 0.003069 | 0.017604 | 0.405576 | 0.376345 | |
STD | 0.003877 | 0.457756 | 0.088091 | 0.338801 | |
Rank | 1 | 3 | 2 | 4 |
Algorithm | RMSE | |||||
---|---|---|---|---|---|---|
NOA | 0.006562 | 5.220376 | 7.865330 | 2.9458 × 10−10 | 0.981397 | 7.92586 × 10−5 |
PSO | 0.000000 | 0.116629 | 9.426077 | 0.000000 | 0.823792 | 1.698016 |
FWA | 0.000000 | 0.153262 | 10.000000 | 3.1557 × 10−10 | 0.999684 | 1.131198 |
WOA | 0.000000 | 0.116653 | 9.425459 | 0.000000 | 0.960865 | 1.698016 |
Algorithm | RMSE | |||||||
---|---|---|---|---|---|---|---|---|
NOA | 0.006562 | 5.229866 | 7.865346 | 2.9392 × 10−10 | 5.4180 × 10−7 | 0.981306 | 3.641440 | 6.02460 × 10−5 |
PSO | 0.046217 | 3000.00000 | 8.037722 | 0.000000 | 1.0000 × 10−6 | 1.000000 | 2.000000 | 1.309913 |
FWA | 0.000335 | 535.789322 | 7.249937 | 4.9392 × 10−10 | 1.1080 × 10−8 | 0.998794 | 2.000811 | 0.817332 |
WOA | 0.046217 | 2332.14650 | 8.037774 | 0.000000 | 1.0000 × 10−6 | 0.112296 | 2.000000 | 1.309914 |
Algorithm | RMSE | |||||||||
---|---|---|---|---|---|---|---|---|---|---|
NOA | 0.006564 | 5.210821 | 7.865464 | 2.9270 × 10−10 | 8.2069 × 10−7 | 9.1951 × 10−7 | 0.981139 | 8.745928 | 8.109913 | 6.23616 × 10−5 |
PSO | 0.006739 | 100.00000 | 7.824180 | 0.000000 | 1.0000 × 10−6 | 1.4708 × 10−11 | 1.000000 | 1.691382 | 0.877124 | 0.013344 |
FWA | 0.004407 | 62.997622 | 7.939448 | 0.000000 | 1.0000 × 10−6 | 1.0000 × 10−6 | 0.556490 | 2.035365 | 1.483360 | 0.106027 |
WOA | 0.006551 | 93.154950 | 7.813773 | 4.6284 × 10−10 | 9.3795 × 10−7 | 5.1560 × 10−9 | 1.000000 | 9.460711 | 9.315814 | 0.019484 |
Parameters | Lower Bound | Upper Bound |
---|---|---|
0 | 10 | |
0 | 3000 | |
0 | 10 | |
0 | 1 | |
0 | 10 |
Algorithm | SDM | DDM | TDM | AVG-Time | RANK |
---|---|---|---|---|---|
NOA | 406.19 | 404.87 | 729.26 | 513.44 | 1 |
PSO | 4279.71 | 6378.25 | 4177.62 | 4945.19 | 3 |
FWA | 4957.14 | 9037.98 | 12516.82 | 8837.32 | 4 |
WOA | 2262.39 | 2263.33 | 4610.02 | 3045.24 | 2 |
NOA vs. | PSO | h | FWA | h | WOA | h |
---|---|---|---|---|---|---|
SDM | 3.01985 × 10−11 | 1 | 1.91209 × 10−9 | 1 | 3.01985 × 10−11 | 1 |
DDM | 2.97473 × 10−11 | 1 | 1.90126 × 10−9 | 1 | 3.00270 × 10−11 | 1 |
TDM | 2.50779 × 10−11 | 1 | 2.80032 × 10−11 | 1 | 3.00098 × 10−11 | 1 |
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Duan, Z.; Yu, H.; Zhang, Q.; Tian, L. Parameter Extraction of Solar Photovoltaic Model Based on Nutcracker Optimization Algorithm. Appl. Sci. 2023, 13, 6710. https://doi.org/10.3390/app13116710
Duan Z, Yu H, Zhang Q, Tian L. Parameter Extraction of Solar Photovoltaic Model Based on Nutcracker Optimization Algorithm. Applied Sciences. 2023; 13(11):6710. https://doi.org/10.3390/app13116710
Chicago/Turabian StyleDuan, Zhenjiang, Hui Yu, Qi Zhang, and Li Tian. 2023. "Parameter Extraction of Solar Photovoltaic Model Based on Nutcracker Optimization Algorithm" Applied Sciences 13, no. 11: 6710. https://doi.org/10.3390/app13116710
APA StyleDuan, Z., Yu, H., Zhang, Q., & Tian, L. (2023). Parameter Extraction of Solar Photovoltaic Model Based on Nutcracker Optimization Algorithm. Applied Sciences, 13(11), 6710. https://doi.org/10.3390/app13116710