Parameter Estimation of Three-Diode Photovoltaic Model Using Reinforced Learning-Based Parrot Optimizer with an Adaptive Secant Method
Abstract
:1. Introduction
- Development of a new variant of the parrot optimizer (PO) using a reinforcement learning-based method for solving real-time engineering problems.
- Development of a new adaptive secant method to improve the solution diversity and reduce the computational time.
- Validation of the proposed algorithm through simulations of different operating conditions.
- Performance comparison among other reputed algorithms.
2. Literature Review
3. Mathematical Modelling and Problem Formulation
3.1. Three-Diode Photovoltaic Model
3.2. Problem Formulation
4. Proposed Reinforced Learning-Based Parrot Optimizer
4.1. Parrot Optimizer
Algorithm 1: Pseudo-code for the PO algorithm |
Initialize PO parameters Randomly initialize the positions of solutions For do Calculate the fitness function for each solution Determine the best and worst positions among the solutions For do Randomly select a strategy from 1 to 4 (Uniform random distribution, i.e., ). If equals 1 (Foraging Behavior) Update the position according to Equation (16). Else If equals 2 (Staying Behavior) Update the position according to Equation (18). Else If equals 3 (Communicating Behavior) Update the position according to Equation (19). Else If equals 4 (Fear of Strangers Behavior) Update the position according to Equation (20). End If End For Return the best solution found End For |
4.2. Reinforcement Learning-Based Parrot Optimizer
Algorithm 2: Pseudo-code of the RL-based parrot optimizer (RLPO) |
Initialize the parameters of the proposed algorithm (, , , , , and ) Initialize population positions within [, ] and evaluate the fitness of each parrot Initialize Q-values for each of the 4 behaviours For do For do Select behaviour for parrot using an ε-greedy strategy based on Q-values Apply behaviour b to update position considering boundaries Evaluate the new fitness of parrot If new fitness is better than previous: Update the parrot’s position and fitness Calculate reward based on improvement Else: Calculate penalty Update Q-value based on the received reward or penalty If new fitness is better than best fitness: Update global best with new position and fitness Update to decrease exploration over time Return: Global best as the best solution found and its fitness as the best score. |
4.3. Time and Space Complexity
5. Results and Discussions
- RMSE: Quantifies the discrepancies between the model’s predictions and the actual observed values, calculated as .
- Relative Error (RE): Provides an error measurement relative to the true value, calculated as .
- Absolute Error (AE): Directly measures the magnitude of error, computed as .
- Determination Coefficient (R2): Illustrates the variance percentage in the dependent variable that can be predicted from the independent variable(s), with .
- Mean Bias Error (MBE): Signifies the model’s average bias in predictions, determined by .
- Standard Deviation (STD): Assesses the variability or dispersion among a set of values.
Parameters | Specifications |
---|---|
Maximum power voltage | 16.6 V |
Maximum power current | 2.41 A |
Maximum power | 40 W |
Open-circuit voltage | 23.3 V |
Short-circuit current | 2.68 A |
Temperature coefficient of open-circuit voltage | −100 × 10−3 V/°C |
Temperature coefficient of short-circuit current | 0.35 × 10−3 A/°C |
1000 W/m2 | 25 °C | |||||||
---|---|---|---|---|---|---|---|---|
Operating conditions | 25 °C | 40 °C | 50 °C | 70 °C | 800 W/m2 | 600 W/m2 | 400 W/m2 | 200 W/m2 |
C1 | C2 | C3 | C4 | C5 | C6 | C7 | C8 | |
Data samples | 26 | 25 | 23 | 22 | 26 | 25 | 25 | 23 |
6. Conclusions and Recommendations
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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Algorithm | Parameters | Values |
---|---|---|
PO | 1.5 | |
RLPO | β | 1.5 |
α | 0.25 | |
γ | 0.65 | |
RLGWO | a | Linearly decreases from 2 to 0 |
α | 0.25 | |
γ | 0.65 | |
RLPSO | ω | 0.9 |
and | 2 | |
0.25 | ||
0.65 | ||
OBEDO | 0.5 | |
OBGBO | 0.01 | |
0.5 | ||
LSMA | 0.03 | |
Linearly decreases from 1 to 0 | ||
HDE | p | 0.1 |
H | 5 |
Case Study | Algorithm | Iph (A) | Isd1 (A) | Rse (Ω) | Rsh (Ω) | n1 | Isd2 (A) | n2 | Isd3 (A) | n3 |
---|---|---|---|---|---|---|---|---|---|---|
C1 | RLPO | 2.6760 | 8.63 × 10−9 | 1.1193 | 354.31 | 4.1887 | 1.82 × 10−7 | 4.9995 | 1.45 × 10−6 | 1.7439 |
PO | 2.6606 | 1.00 × 10−4 | 1.1600 | 1941.43 | 4.8415 | 1.53 × 10−7 | 1.5238 | 1.00 × 10−4 | 3.0125 | |
OBGBO | 2.6703 | 1.51 × 10−5 | 1.0480 | 483.09 | 4.0874 | 2.60 × 10−6 | 1.8145 | 5.82 × 10−5 | 4.7785 | |
RLPSO | 2.6573 | 3.74 × 10−6 | 0.7502 | 2597.55 | 2.3719 | 1.71 × 10−7 | 2.3369 | 2.15 × 10−5 | 2.1317 | |
LSMA | −0.2566 | 2.67 × 10−1 | 264.71 | 835.83 | 1.0788 | 5.41 × 10−1 | 6.2599 | −1.00 × 102 | 2.5847 | |
RLGWO | 2.6589 | 3.74 × 10−5 | 0.9445 | 1515.05 | 4.1075 | 6.57 × 10−6 | 1.9426 | 2.21 × 10−5 | 3.2635 | |
HDE | 2.6760 | 4.67 × 10−6 | 1.1202 | 355.87 | 4.9851 | 1.43 × 10−6 | 1.7422 | 4.31 × 10−6 | 4.9909 | |
OBEDO | 2.6736 | 1.00 × 10−4 | 1.1009 | 422.17 | 5.0000 | 1.00 × 10−4 | 5.0000 | 1.47 × 10−6 | 1.7454 | |
C2 | RLPO | 2.6812 | 5.41 × 10−6 | 1.1334 | 358.21 | 1.7165 | 2.67 × 10−11 | 4.6837 | 0.00 × 100 | 4.9991 |
PO | 2.6778 | 9.94 × 10−5 | 1.0731 | 455.31 | 5.0000 | 8.22 × 10−6 | 1.7706 | 9.96 × 10−5 | 5.0000 | |
OBGBO | 2.6734 | 7.61 × 10−6 | 1.0039 | 560.96 | 4.9695 | 1.36 × 10−5 | 3.0469 | 1.36 × 10−5 | 1.8390 | |
RLPSO | 2.6674 | 9.73 × 10−5 | 0.9409 | 4314.89 | 2.9302 | 3.47 × 10−5 | 2.8206 | 2.22 × 10−5 | 1.9398 | |
LSMA | 2.3675 | 2.08 × 10−1 | 158.60 | 4330.35 | 0.4133 | −6.81 × 10−1 | 0.6192 | −8.02 × 10−1 | 3.1605 | |
RLGWO | 2.6660 | 4.27 × 10−5 | 1.0564 | 1733.81 | 3.1788 | 3.32 × 10−6 | 1.6777 | 5.09 × 10−5 | 2.4430 | |
HDE | 2.6812 | 1.62 × 10−10 | 1.1334 | 358.21 | 4.8665 | 9.62 × 10−10 | 4.9997 | 5.41 × 10−6 | 1.7165 | |
OBEDO | 2.6808 | 1.00 × 10−4 | 1.1339 | 374.92 | 5.0000 | 0.00 × 100 | 5.0000 | 5.19 × 10−6 | 1.7113 | |
C3 | RLPO | 2.6904 | 1.69 × 10−13 | 1.1229 | 317.75 | 4.5116 | 2.33 × 10−5 | 1.7492 | 3.40 × 10−14 | 4.9967 |
PO | 2.6797 | 1.00 × 10−4 | 0.9782 | 728.09 | 4.9310 | 3.72 × 10−5 | 3.7480 | 6.75 × 10−5 | 1.9169 | |
OBGBO | 2.6807 | 1.49 × 10−5 | 1.1237 | 549.94 | 3.2956 | 4.29 × 10−6 | 5.0000 | 2.95 × 10−5 | 1.7860 | |
RLPSO | 2.6735 | 6.86 × 10−5 | 0.9441 | 2937.45 | 3.5476 | 6.68 × 10−5 | 2.5268 | 6.70 × 10−5 | 1.9276 | |
LSMA | 3.0902 | −1.18 × 101 | 179.40 | 2461.61 | 0.6797 | 5.61 × 100 | 2.2959 | 1.07 × 101 | 1.1642 | |
RLGWO | 2.6797 | 2.47 × 10−7 | 0.9555 | 787.59 | 3.3146 | 3.68 × 10−5 | 1.8488 | 9.15 × 10−5 | 2.3270 | |
HDE | 2.6904 | 9.61 × 10−8 | 1.1229 | 317.76 | 5.0000 | 6.86 × 10−12 | 4.9992 | 2.33 × 10−5 | 1.7492 | |
OBEDO | 2.6891 | 1.00 × 10−4 | 1.1039 | 344.31 | 5.0000 | 2.63 × 10−5 | 1.7662 | 0.00 × 100 | 1.0000 | |
C4 | RLPO | 2.6930 | 6.97 × 10−5 | 1.1472 | 365.82 | 1.6924 | 6.14 × 10−5 | 3.5672 | 9.89 × 10−5 | 3.4249 |
PO | 2.6856 | 2.59 × 10−5 | 1.1997 | 591.43 | 4.9982 | 1.00 × 10−4 | 2.3705 | 4.59 × 10−5 | 1.6406 | |
OBGBO | 2.6913 | 5.44 × 10−5 | 1.1271 | 375.29 | 1.6973 | 4.02 × 10−5 | 1.8372 | 3.12 × 10−5 | 5.0000 | |
RLPSO | 2.6795 | 9.99 × 10−5 | 0.9054 | 2834.31 | 1.8913 | 9.99 × 10−5 | 1.9207 | 9.99 × 10−5 | 2.0497 | |
LSMA | 2.2897 | −9.95 × 10−1 | 170.01 | 4844.27 | 0.6088 | 7.19 × 10−1 | 1.7404 | −5.39 × 10−1 | 4.2969 | |
RLGWO | 2.6850 | 2.34 × 10−5 | 1.1040 | 657.98 | 1.9749 | 9.84 × 10−5 | 1.7591 | 3.36 × 10−7 | 3.0636 | |
HDE | 2.6926 | 1.00 × 10−4 | 1.1537 | 383.14 | 3.2120 | 9.77 × 10−5 | 2.8335 | 5.90 × 10−5 | 1.6692 | |
OBEDO | 2.6930 | 7.92 × 10−5 | 1.1374 | 355.15 | 1.7113 | 0.00 × 100 | 5.0000 | 9.66 × 10−5 | 5.0000 | |
C5 | RLPO | 2.6760 | 1.45 × 10−6 | 1.1194 | 354.37 | 1.7438 | 1.53 × 10−7 | 5.0000 | 5.37 × 10−7 | 4.9092 |
PO | 2.6616 | 1.00 × 10−4 | 1.2826 | 1719.81 | 2.9201 | 1.21 × 10−7 | 4.9998 | 1.02 × 10−8 | 1.3157 | |
OBGBO | 2.6707 | 1.23 × 10−5 | 1.0473 | 540.24 | 4.9386 | 3.12 × 10−5 | 2.7935 | 1.65 × 10−6 | 1.7687 | |
RLPSO | 2.6661 | 3.54 × 10−6 | 0.6633 | 967.37 | 1.9782 | 3.88 × 10−5 | 2.3644 | 3.14 × 10−5 | 2.8067 | |
LSMA | 2.4251 | 4.82 × 10−1 | 212.85 | 1362.59 | 1.2111 | −7.69 × 100 | 0.8734 | 1.64 × 100 | 3.1965 | |
RLGWO | 2.6655 | 2.09 × 10−5 | 0.8595 | 757.83 | 3.0206 | 1.81 × 10−6 | 1.8837 | 9.80 × 10−6 | 2.0864 | |
HDE | 2.6758 | 2.82 × 10−5 | 1.1227 | 361.16 | 4.8604 | 1.36 × 10−6 | 1.7370 | 5.55 × 10−6 | 4.9872 | |
OBEDO | 2.6736 | 0.00 × 100 | 1.0539 | 393.97 | 5.0000 | 0.00 × 100 | 5.0000 | 2.51 × 10−6 | 1.8096 | |
C6 | RLPO | 2.1382 | 1.09 × 10−5 | 1.1390 | 331.24 | 4.8464 | 1.04 × 10−6 | 1.7062 | 0.00 × 100 | 1.0000 |
PO | 2.1241 | 6.31 × 10−5 | 1.0332 | 815.92 | 4.2965 | 3.35 × 10−6 | 1.8547 | 9.93 × 10−6 | 4.2683 | |
OBGBO | 2.1316 | 1.96 × 10−5 | 1.0146 | 422.86 | 3.2827 | 1.68 × 10−6 | 1.7590 | 1.12 × 10−5 | 5.0000 | |
RLPSO | 2.1152 | 7.21 × 10−6 | 0.8159 | 4097.27 | 3.6336 | 1.08 × 10−5 | 2.0172 | 8.75 × 10−10 | 4.0451 | |
LSMA | −0.4905 | −1.32 × 10−1 | 939.53 | 2581.04 | 3.0508 | 1.60 × 10−1 | 5.1556 | 3.84 × 10−1 | 5.5430 | |
RLGWO | 2.1298 | 7.75 × 10−6 | 0.8232 | 549.53 | 1.9696 | 2.73 × 10−5 | 4.3172 | 4.39 × 10−5 | 3.7817 | |
HDE | 2.1382 | 1.06 × 10−6 | 1.1369 | 330.15 | 1.7092 | 1.76 × 10−6 | 4.9983 | 1.19 × 10−8 | 4.9960 | |
OBEDO | 2.1264 | 0.00 × 100 | 0.6718 | 686.15 | 1.0000 | 1.88 × 10−5 | 2.1095 | 0.00 × 100 | 5.0000 | |
C7 | RLPO | 1.6049 | 6.05 × 10−7 | 1.1232 | 346.03 | 5.0000 | 1.36 × 10−6 | 1.7386 | 1.03 × 10−9 | 4.9697 |
PO | 1.5977 | 4.68 × 10−6 | 1.0509 | 537.65 | 1.9933 | 3.46 × 10−5 | 3.5136 | 9.06 × 10−8 | 1.5340 | |
OBGBO | 1.6011 | 1.40 × 10−6 | 1.1086 | 450.23 | 1.7461 | 3.92 × 10−5 | 4.5916 | 1.80 × 10−5 | 3.0373 | |
RLPSO | 1.6021 | 1.19 × 10−5 | 0.6476 | 462.08 | 2.0546 | 1.01 × 10−5 | 3.5326 | 8.38 × 10−5 | 3.6943 | |
LSMA | −8.1819 | 5.71 × 102 | 201.58 | 1302.96 | 1.7744 | −9.8 × 10−1 | 5.6157 | 3.63 × 100 | 0.4987 | |
RLGWO | 1.5960 | 4.15 × 10−5 | 0.8056 | 683.76 | 3.0592 | 8.54 × 10−6 | 2.4768 | 3.89 × 10−6 | 1.8977 | |
HDE | 1.6049 | 1.29 × 10−6 | 1.1286 | 349.73 | 1.7319 | 2.22 × 10−7 | 4.9161 | 2.55 × 10−5 | 4.9737 | |
OBEDO | 1.6011 | 0.00 × 100 | 0.9074 | 429.32 | 5.0000 | 4.76 × 10−6 | 1.9049 | 0.00 × 100 | 5.0000 | |
C8 | RLPO | 1.0679 | 1.00 × 10−4 | 1.2094 | 369.35 | 4.9767 | 1.04 × 10−6 | 1.7080 | 5.62 × 10−8 | 4.7167 |
PO | 1.0626 | 1.34 × 10−5 | 0.9009 | 504.81 | 3.7927 | 1.00 × 10−4 | 4.9972 | 4.12 × 10−6 | 1.8934 | |
OBGBO | 1.0650 | 4.26 × 10−5 | 0.6733 | 411.73 | 4.9926 | 7.44 × 10−5 | 5.0000 | 4.45 × 10−6 | 1.8951 | |
RLPSO | 1.0586 | 1.89 × 10−5 | 0.0814 | 823.60 | 2.4394 | 4.11 × 10−5 | 2.3835 | 1.81 × 10−6 | 2.8115 | |
LSMA | 2.0078 | 8.84 × 100 | 378.32 | 1937.33 | 0.6172 | 2.36 × 10−1 | 6.2047 | 1.27 × 100 | 3.3094 | |
RLGWO | 1.0631 | 3.95 × 10−6 | 0.2145 | 437.95 | 3.0625 | 5.29 × 10−5 | 3.4349 | 9.20 × 10−6 | 2.0084 | |
HDE | 1.0679 | 9.41 × 10−5 | 1.2148 | 369.14 | 4.9431 | 1.02 × 10−6 | 1.7050 | 5.77 × 10−6 | 4.8998 | |
OBEDO | 1.0651 | 3.27 × 10−6 | 0.8402 | 432.65 | 1.8559 | 1.00 × 10−4 | 5.0000 | 1.00 × 10−4 | 5.0000 |
Metrics | Algorithm | RLPO | PO | OBGBO | RLPSO | LSMA | RLGWO | HDE | OBEDO |
---|---|---|---|---|---|---|---|---|---|
RMSE | C1 | 6.473 × 10−6 | 6.992 × 10−6 | 5.984 × 10−6 | 4.460 × 10−6 | 5.110 × 10−6 | 4.060 × 10−6 | 2.136 × 10−6 | 1.052 × 10−6 |
C2 | 4.561 × 10−5 | 1.677 × 10−5 | 3.619 × 10−5 | 2.823 × 10−5 | 4.579 × 10−5 | 1.840 × 10−5 | 9.881 × 10−6 | 1.592 × 10−6 | |
C3 | 2.291 × 10−5 | 3.137 × 10−5 | 3.438 × 10−5 | 1.419 × 10−5 | 2.622 × 10−5 | 1.311 × 10−5 | 7.876 × 10−6 | 2.535 × 10−6 | |
C4 | 9.088 × 10−5 | 8.860 × 10−5 | 5.287 × 10−5 | 4.960 × 10−5 | 7.688 × 10−5 | 3.726 × 10−5 | 2.336 × 10−6 | 1.328 × 10−5 | |
C5 | 3.119 × 10−5 | 4.632 × 10−5 | 2.785 × 10−5 | 2.591 × 10−5 | 2.855 × 10−5 | 1.367 × 10−5 | 4.821 × 10−6 | 1.976 × 10−6 | |
C6 | 6.355 × 10−5 | 4.707 × 10−5 | 4.115 × 10−5 | 2.282 × 10−5 | 4.107 × 10−5 | 2.862 × 10−5 | 1.558 × 10−5 | 1.932 × 10−6 | |
C7 | 6.471 × 10−6 | 6.992 × 10−6 | 5.984 × 10−6 | 4.654 × 10−6 | 5.113 × 10−6 | 4.064 × 10−6 | 2.137 × 10−6 | 1.063 × 10−6 | |
C8 | 1.093 × 10−5 | 7.258 × 10−6 | 7.531 × 10−6 | 4.950 × 10−6 | 5.638 × 10−5 | 1.520 × 10−5 | 6.316 × 10−6 | 2.041 × 10−6 | |
Mean | 4.533 × 10−6 | 2.531 × 10−5 | 1.907 × 10−5 | 5.409 × 10−5 | 2.254 × 10−5 | 3.272 × 10−5 | 4.560 × 10−6 | 1.383 × 10−5 | |
R2 | C1 | 1.00000 | 0.98751 | 0.98987 | 0.99000 | 0.96588 | 0.98756 | 0.98985 | 0.98756 |
C2 | 1.00000 | 0.98746 | 0.98746 | 0.98000 | 0.97459 | 1.00000 | 1.00000 | 0.99875 | |
C3 | 1.00000 | 0.99000 | 0.99874 | 0.96700 | 0.96651 | 0.97530 | 1.00000 | 0.98875 | |
C4 | 1.00000 | 0.99995 | 0.96589 | 0.98970 | 0.96524 | 0.98786 | 1.00000 | 0.98369 | |
C5 | 1.00000 | 1.00000 | 0.97854 | 0.98966 | 0.97846 | 0.94759 | 1.00000 | 0.98746 | |
C6 | 1.00000 | 0.97854 | 0.99357 | 0.99000 | 0.97419 | 0.99875 | 0.98573 | 0.97336 | |
C7 | 1.00000 | 1.00000 | 1.00000 | 0.99000 | 0.96423 | 0.99854 | 1.00000 | 0.98756 | |
C8 | 1.00000 | 0.96589 | 0.98556 | 1.00000 | 0.97856 | 1.00000 | 0.98578 | 1.00000 | |
Mean | 1.00000 | 0.98867 | 0.98745 | 0.98704 | 0.97096 | 0.98695 | 0.99517 | 0.98839 | |
MBE | C1 | 1.001 × 10−9 | 3.014 × 10−8 | 3.934 × 10−8 | 1.174 × 10−6 | 2.260 × 10−8 | 1.621 × 10−7 | 1.031 × 10−9 | 4.266 × 10−9 |
C2 | 1.603 × 10−9 | 5.183 × 10−8 | 3.046 × 10−7 | 2.041 × 10−7 | 4.400 × 10−8 | 1.025 × 10−7 | 1.603 × 10−9 | 1.662 × 10−9 | |
C3 | 4.003 × 10−9 | 1.464 × 10−7 | 2.213 × 10−8 | 2.364 × 10−7 | 1.877 × 10−8 | 2.253 × 10−7 | 4.001 × 10−9 | 1.138 × 10−8 | |
C4 | 2.791 × 10−9 | 1.134 × 10−7 | 0.237 × 10−8 | 1.375 × 10−6 | 1.683 × 10−8 | 7.794 × 10−9 | 3.120 × 10−9 | 1.129 × 10−9 | |
C5 | 1.679 × 10−9 | 5.167 × 10−8 | 2.412 × 10−7 | 7.605 × 10−7 | 2.387 × 10−8 | 4.554 × 10−7 | 1.523 × 10−9 | 1.258 × 10−6 | |
C6 | 9.322 × 10−10 | 1.465 × 10−8 | 8.857 × 10−9 | 9.142 × 10−8 | 1.007 × 10−8 | 4.616 × 10−8 | 9.579 × 10−10 | 1.672 × 10−8 | |
C7 | 7.300 × 10−9 | 1.056 × 10−8 | 2.768 × 10−7 | 1.841 × 10−7 | 3.434 × 10−9 | 1.660 × 10−6 | 7.881 × 10−9 | 4.303 × 10−8 | |
C8 | 5.221 × 10−10 | 3.134 × 10−9 | 9.258 × 10−9 | 2.308 × 10−7 | 1.771 × 10−9 | 6.966 × 10−9 | 4.918 × 10−10 | 6.066 × 10−9 | |
Mean | 2.479 × 10−9 | 5.273 × 10−8 | 1.143 × 10−7 | 5.321 × 10−7 | 1.767 × 10−8 | 3.333 × 10−7 | 2.576 × 10−9 | 1.677 × 10−7 | |
AE | C1 | 5.444 × 10−6 | 3.436 × 10−5 | 1.955 × 10−5 | 7.776 × 10−5 | 1.992 × 10−5 | 5.479 × 10−5 | 5.439 × 10−6 | 8.474 × 10−6 |
C2 | 5.635 × 10−6 | 1.447 × 10−5 | 2.647 × 10−5 | 7.476 × 10−5 | 4.340 × 10−5 | 3.870 × 10−5 | 5.635 × 10−6 | 6.027 × 10−6 | |
C3 | 4.357 × 10−6 | 3.194 × 10−5 | 2.911 × 10−5 | 4.482 × 10−5 | 1.875 × 10−5 | 3.695 × 10−5 | 4.357 × 10−6 | 5.734 × 10−6 | |
C4 | 3.684 × 10−6 | 2.445 × 10−5 | 1.271 × 10−5 | 3.867 × 10−5 | 1.813 × 10−5 | 1.706 × 10−5 | 3.725 × 10−6 | 3.695 × 10−6 | |
C5 | 4.358 × 10−6 | 3.652 × 10−5 | 1.956 × 10−5 | 6.285 × 10−5 | 2.396 × 10−5 | 3.544 × 10−5 | 4.368 × 10−6 | 4.794 × 10−5 | |
C6 | 3.588 × 10−6 | 1.532 × 10−5 | 1.159 × 10−5 | 2.997 × 10−5 | 9.836 × 10−6 | 2.512 × 10−5 | 3.572 × 10−6 | 1.284 × 10−5 | |
C7 | 1.596 × 10−6 | 8.380 × 10−6 | 5.890 × 10−6 | 2.062 × 10−5 | 2.970 × 10−6 | 1.065 × 10−5 | 1.782 × 10−6 | 5.244 × 10−6 | |
C8 | 9.037 × 10−7 | 1.348 × 10−6 | 2.126 × 10−6 | 1.176 × 10−5 | 1.850 × 10−6 | 1.536 × 10−6 | 8.806 × 10−7 | 1.564 × 10−6 | |
Mean | 3.696 × 10−6 | 2.085 × 10−5 | 1.588 × 10−5 | 4.515 × 10−5 | 1.735 × 10−5 | 2.753 × 10−5 | 3.720 × 10−6 | 1.144 × 10−5 | |
RE | C1 | 2.362 × 10−7 | 2.081 × 10−8 | 4.155 × 10−6 | 1.932 × 10−5 | 1.021 × 10−5 | 5.263 × 10−6 | 2.573 × 10−7 | 8.966 × 10−7 |
C2 | 4.125 × 10−8 | 5.309 × 10−6 | 1.550 × 10−5 | 5.027 × 10−6 | 2.018 × 10−5 | 5.993 × 10−6 | 4.264 × 10−8 | 1.104 × 10−7 | |
C3 | 7.627 × 10−7 | 7.183 × 10−6 | 1.804 × 10−8 | 9.076 × 10−6 | 9.896 × 10−6 | 7.989 × 10−6 | 7.616 × 10−7 | 1.869 × 10−6 | |
C4 | 1.185 × 10−6 | 9.482 × 10−6 | 1.375 × 10−6 | 3.380 × 10−5 | 9.972 × 10−6 | 4.169 × 10−7 | 1.196 × 10−6 | 5.150 × 10−7 | |
C5 | 5.813 × 10−7 | 1.539 × 10−6 | 1.397 × 10−5 | 1.682 × 10−5 | 1.355 × 10−5 | 1.363 × 10−5 | 5.124 × 10−7 | 1.921 × 10−5 | |
C6 | 1.029 × 10−7 | 2.205 × 10−8 | 1.272 × 10−6 | 4.723 × 10−7 | 7.510 × 10−6 | 3.522 × 10−7 | 1.248 × 10−7 | 3.604 × 10−6 | |
C7 | 1.628 × 10−6 | 8.521 × 10−8 | 1.179 × 10−5 | 4.387 × 10−6 | 3.887 × 10−6 | 2.740 × 10−5 | 1.706 × 10−6 | 4.271 × 10−6 | |
C8 | 2.950 × 10−8 | 4.883 × 10−7 | 3.764 × 10−7 | 7.890 × 10−6 | 4.021 × 10−6 | 7.469 × 10−7 | 5.021 × 10−9 | 8.069 × 10−7 | |
Mean | 5.709 × 10−7 | 3.016 × 10−6 | 6.056 × 10−6 | 1.210 × 10−5 | 9.904 × 10−6 | 7.723 × 10−6 | 5.757 × 10−7 | 3.911 × 10−6 | |
STD | C1 | 1.946 × 10−5 | 2.976 × 10−5 | 2.398 × 10−5 | 1.493 × 10−4 | 2.150 × 10−5 | 1.227 × 10−4 | 2.649 × 10−5 | 1.417 × 10−4 |
C2 | 1.189 × 10−5 | 2.076 × 10−5 | 2.561 × 10−5 | 1.111 × 10−4 | 2.127 × 10−5 | 1.431 × 10−4 | 2.010 × 10−5 | 2.304 × 10−5 | |
C3 | 5.029 × 10−6 | 1.820 × 10−5 | 1.116 × 10−5 | 1.424 × 10−4 | 2.412 × 10−5 | 5.056 × 10−5 | 1.418 × 10−5 | 1.571 × 10−5 | |
C4 | 1.539 × 10−7 | 2.818 × 10−5 | 3.140 × 10−5 | 7.480 × 10−5 | 1.292 × 10−7 | 3.129 × 10−5 | 1.466 × 10−5 | 7.206 × 10−5 | |
C5 | 4.032 × 10−6 | 1.220 × 10−5 | 2.078 × 10−5 | 8.684 × 10−5 | 1.231 × 10−5 | 1.976 × 10−5 | 2.451 × 10−5 | 7.062 × 10−5 | |
C6 | 7.109 × 10−8 | 1.004 × 10−5 | 1.204 × 10−5 | 4.370 × 10−5 | 2.821 × 10−5 | 7.439 × 10−6 | 1.141 × 10−5 | 1.498 × 10−5 | |
C7 | 4.026 × 10−6 | 7.703 × 10−6 | 5.345 × 10−6 | 1.964 × 10−5 | 6.327 × 10−6 | 5.998 × 10−6 | 5.236 × 10−6 | 9.279 × 10−6 | |
C8 | 2.115 × 10−7 | 4.039 × 10−6 | 1.854 × 10−6 | 1.428 × 10−6 | 3.147 × 10−7 | 4.688 × 10−6 | 5.606 × 10−7 | 5.439 × 10−6 | |
Mean | 5.609 × 10−6 | 1.636 × 10−5 | 1.652 × 10−5 | 7.865 × 10−5 | 3.040 × 10−5 | 4.819 × 10−5 | 1.464 × 10−5 | 4.410 × 10−5 | |
RT | C1 | 22.436 | 22.413 | 47.296 | 23.272 | 70.407 | 22.876 | 23.965 | 59.296 |
C2 | 22.007 | 21.996 | 46.713 | 24.231 | 70.220 | 23.159 | 23.924 | 58.494 | |
C3 | 20.539 | 20.294 | 43.163 | 21.677 | 65.233 | 21.953 | 22.178 | 54.849 | |
C4 | 22.354 | 22.328 | 46.771 | 24.573 | 70.618 | 23.586 | 24.388 | 59.429 | |
C5 | 21.214 | 21.004 | 44.198 | 21.772 | 67.547 | 22.080 | 22.639 | 55.728 | |
C6 | 21.793 | 21.491 | 44.792 | 22.523 | 67.770 | 23.542 | 23.219 | 56.557 | |
C7 | 16.443 | 16.234 | 34.593 | 17.579 | 53.683 | 18.657 | 18.300 | 44.398 | |
C8 | 21.856 | 21.688 | 46.009 | 22.786 | 69.325 | 22.891 | 23.395 | 58.203 | |
Mean | 21.080 | 20.931 | 44.192 | 22.302 | 66.850 | 22.343 | 22.751 | 55.869 |
Algorithms | C1 | C2 | C3 | C4 | C5 | C6 | C7 | C8 | Average |
---|---|---|---|---|---|---|---|---|---|
RLPO | 23.4365 | 23.0073 | 21.5385 | 22.1042 | 22.2135 | 22.7927 | 16.4427 | 22.8563 | 21.7990 |
PO | 23.4125 | 22.9958 | 21.7938 | 22.1167 | 21.8042 | 22.0906 | 16.7344 | 22.8875 | 21.7294 |
OBGBO | 70.4073 | 70.2198 | 65.2333 | 67.0750 | 67.5469 | 67.7698 | 53.6833 | 69.3250 | 66.4076 |
RLPSO | 59.2958 | 58.4938 | 54.8490 | 56.0344 | 55.7281 | 56.5573 | 44.3979 | 58.2031 | 55.4449 |
LSMA | 47.2958 | 46.7125 | 43.1625 | 44.6479 | 44.1979 | 44.7917 | 34.5927 | 46.0094 | 43.9263 |
RLGWO | 22.8760 | 23.1594 | 21.9531 | 22.2281 | 22.0802 | 22.5417 | 17.6573 | 22.8906 | 21.9233 |
HDE | 23.9646 | 23.9240 | 22.1781 | 22.8760 | 22.6385 | 23.2188 | 18.3000 | 23.3948 | 22.5618 |
OBEDO | 23.2719 | 23.2313 | 21.6771 | 22.2615 | 21.7719 | 22.5229 | 17.5792 | 22.7865 | 21.8878 |
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Kullampalayam Murugaiyan, N.; Chandrasekaran, K.; Devapitchai, M.M.; Senjyu, T. Parameter Estimation of Three-Diode Photovoltaic Model Using Reinforced Learning-Based Parrot Optimizer with an Adaptive Secant Method. Sustainability 2024, 16, 10603. https://doi.org/10.3390/su162310603
Kullampalayam Murugaiyan N, Chandrasekaran K, Devapitchai MM, Senjyu T. Parameter Estimation of Three-Diode Photovoltaic Model Using Reinforced Learning-Based Parrot Optimizer with an Adaptive Secant Method. Sustainability. 2024; 16(23):10603. https://doi.org/10.3390/su162310603
Chicago/Turabian StyleKullampalayam Murugaiyan, Nandhini, Kumar Chandrasekaran, Magdalin Mary Devapitchai, and Tomonobu Senjyu. 2024. "Parameter Estimation of Three-Diode Photovoltaic Model Using Reinforced Learning-Based Parrot Optimizer with an Adaptive Secant Method" Sustainability 16, no. 23: 10603. https://doi.org/10.3390/su162310603
APA StyleKullampalayam Murugaiyan, N., Chandrasekaran, K., Devapitchai, M. M., & Senjyu, T. (2024). Parameter Estimation of Three-Diode Photovoltaic Model Using Reinforced Learning-Based Parrot Optimizer with an Adaptive Secant Method. Sustainability, 16(23), 10603. https://doi.org/10.3390/su162310603