Evaluation of Weighted Mean of Vectors Algorithm for Identification of Solar Cell Parameters
Abstract
:1. Introduction
- A novel optimization method (INFO) is applied to estimate the variables of three models of solar cell: the three-diode model of solar cell (TDMSC), double-diode model of solar cell (DDMSC), and single-diode model of solar cell (SDMSC).
- The fitness function of the identification work is to minimize the RSME between the measured data of current and the data of simulated current based on the parameters identified from the algorithms.
- The INFO technique is compared with another seven methods: Harris hawk optimization, tunicate swarm algorithm, sine–cosine algorithm, moth–flame optimizer, grey wolf optimization, chimp optimization algorithm, and Runge–Kutta Optimization.
- The statistical analysis is applied to measure and assess the performance of the proposed RUN algorithm along with all competing algorithms. The analysis contains several points, such as the mean, minimum, maximum, and standard deviation for the objective function over 30 independent runs.
- The fastest and most reliable algorithm is determined according to the convergence and robustness curves for all algorithms.
- The efficiency of the INFO method is also determined based on the absolute error values of current and power among both measured and simulated data.
2. Problem Formulation of Solar Cell Models
2.1. Analysis of SDMCS
2.2. Analysis of DDMSC
2.3. Analysis of TDMSC
3. Fitness Function for Identifying the Parameters of the Solar Cell
4. Weighted Mean Definition
Weighted Mean Definition from a Mathematical Point of View
5. The Weighted Mean from Vectors Algorithm
- Phase 1: Updating rules;
- Phase 2: Vector combination;
- Phase 3: Local search.
5.1. The Initialization Phase
5.2. The Rule-Updating Phase
5.3. The Vector-Combining Phase
5.4. The Local Search Phase
Algorithm 1: The pseudocode for the INFO algorithm |
Set the parameters of and Produce the initial population Compute an objective function value from each vector: . Determine the optimal vector . Do { Choose randomly in the range . Compute by using Equations (10)–(12) and (15)–(17). Update by using Equation (19) and with Equation (24). Compute the solutions and using Equation (23). Compute by using Equation (26). Compute by using Equation (27). Compute by using Equation (27). Compute by using Equation (29). Compute by using Equation (30). Compute the value of objective function, . = Update the optimal vector . } Return the vector as a final solution. |
6. Numerical Analysis of Results
6.1. SDMSC Extracted Results
6.2. DDMSC Extracted Results
6.3. TDMSC Extracted Results
6.4. Statistical Analysis of the Three Solar Cell Models
7. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
Abbreviations
RE | Renewable energy |
SE | Solar energy |
PV | Photovoltaic |
SD | Single-diode |
DD | Double-diode |
TD | Triple-diode |
INFO | Weighted mean of vectors |
HHO | Harris hawk optimization |
TSA | Tunicate swarm algorithm |
SCA | Sine–cosine algorithm |
MFO | Moth–flame optimizer |
GWO | Grey wolf optimization |
ChOA | Chimp optimization algorithm |
RUN | Runge–Kutta optimization |
TDMSC | Three-diode model of solar cell |
DDMSC | Double-diode model of solar cell |
SDMSC | Single-diode model of solar cell |
RMSE | Root-mean-square error |
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Parameters | Lower Bound | Upper Bound |
---|---|---|
0 | 1 | |
0 | 0.5 | |
0 | 1 | |
1 | 2 | |
0 | 100 |
Algorithm | Parameter Setting |
---|---|
INFO | c = 2, d = 4 (Default) |
HHO | E0 ∈ [−1, 1], β = 1.5 (Default) |
TSA | Pmin = 1 and Pmax = 4 (Default) |
RUN | a = 20 and b = 12 (Default) |
GWO | Control parameter (a) linearly decreases from 2 to 0 (default) |
MFO | b = 1 and a linearly decreases from −1 to −2 (default) |
SCA | A = 2 (default) |
ChOA | Control parameter (a) linearly decreases from 2 to 0 (default) |
Method | RMSE | |||||
---|---|---|---|---|---|---|
INFO | 0.760775531 | 3.23 × 10−7 | 1.481183583 | 0.036377093 | 53.71852003 | 0.000986022 |
MFO | 0.760610259 | 4.66 × 10−7 | 1.519075084 | 0.034885349 | 66.30741592 | 0.001211865 |
SCA | 0.756072108 | 5.75 × 10−7 | 1.542488704 | 0.026028415 | 35.73635426 | 0.01342705 |
TSA | 0.7601137 | 6.18 × 10−7 | 1.549825146 | 0.03367546 | 63.2081264 | 0.002027996 |
HHO | 0.759689107 | 1.96 × 10−7 | 1.431980756 | 0.038740252 | 59.89341231 | 0.001721616 |
GWO | 0.760495146 | 4.33 × 10−7 | 1.510919086 | 0.035735604 | 77.00217485 | 0.001428873 |
ChOA | 0.778747386 | 6.84 × 10−7 | 1.561498887 | 0.031486912 | 13.00230926 | 0.013439016 |
RUN | 0.760738786 | 3.73 × 10−7 | 1.495871948 | 0.03578791 | 57.51621103 | 0.001024176 |
Method | RMSE | |||||||
---|---|---|---|---|---|---|---|---|
INFO | 0.760784749 | 9.09 × 10−7 | 1.999999999 | 0.036848784 | 55.72870238 | 2.07 × 10−7 | 1.443467334 | 0.000982755 |
MFO | 0.760573102 | 5.14 × 10−7 | 1.529488629 | 0.034473352 | 70.70524625 | 0 | 2 | 0.001330898 |
SCA | 0.758573427 | 3.27 × 10−7 | 1.479787147 | 0.046141622 | 100 | 0 | 1.299741087 | 0.020743587 |
TSA | 0.759753871 | 3.00 × 10−8 | 1.619380419 | 0.035766388 | 83.19040588 | 3.99 × 10−7 | 1.504899251 | 0.00182302 |
HHO | 0.761355149 | 8.90 × 10−7 | 1.621226033 | 0.031536148 | 88.97195633 | 1.53 × 10−7 | 1.560107435 | 0.002601794 |
GWO | 0.761522609 | 3.42 × 10−8 | 1.973842184 | 0.036949692 | 42.7698821 | 2.62 × 10−7 | 1.460667435 | 0.001163084 |
ChOA | 0.777351746 | 4.64 × 10−7 | 1.519880609 | 0.029571053 | 24.13155704 | 0 | 1.520252231 | 0.015533816 |
RUN | 0.760778654 | 1.90 × 10−7 | 1.488917271 | 0.036170888 | 54.72135704 | 1.50 × 10−7 | 1.483016386 | 0.000990819 |
Method | INFO | MFO | SCA | TSA | HHO | GWO | ChOA | RUN |
---|---|---|---|---|---|---|---|---|
0.760782737 | 7.61 × 10−1 | 7.82 × 10−1 | 0.760787945 | 0.762274159 | 0.761 | 0.75782536 | 0.76078498 | |
1.00 × 10−6 | 2.35 × 10−7 | 0 | 3.92 × 10−8 | 5.71 × 10−7 | 1.41 × 10−7 | 1.53 × 10−9 | 7.65 × 10−9 | |
2 | 1.46 | 1.29 | 1.515945641 | 1.562234058 | 1.42 | 1.091333206 | 1.84021139 | |
0.036874376 | 0.036408874 | 0.036890526 | 0.036128601 | 0.033272778 | 0.037122094 | 0.05449899 | 0.036773835 | |
56.17108115 | 58.79879946 | 53.82857553 | 70.07457274 | 49.82864639 | 66.37293159 | 47.7643334 | 54.00897362 | |
2.16 × 10−17 | 4.89 × 10−7 | 0 | 2.49 × 10−7 | 7.73 × 10−8 | 5.46 × 10−7 | 7.18 × 10−8 | 1.48 × 10−7 | |
2 | 1.980735265 | 1.717307943 | 1.465621068 | 1.515599863 | 1.953366972 | 1.549521311 | 1.42890028 | |
1.98 × 10−7 | 3.50 × 10−7 | 6.85 × 10−7 | 1.11 × 10−7 | 3.11 × 10−40 | 5.41 × 10−7 | 6.54 × 10−9 | 3.02 × 10−7 | |
1.440116403 | 2 | 1.558130572 | 1.85904076 | 1.49038742 | 1.842301795 | 1.618146711 | 1.647232901 | |
RMSE | 0.00098297 | 0.000998934 | 0.015666298 | 0.002159304 | 0.002093376 | 0.001082604 | 0.011807743 | 0.000987658 |
Method | Min | Mean | Max | STD |
---|---|---|---|---|
INFO | 0.000986022 | 0.000986022 | 0.000986022 | 4.50 × 10−12 |
MFO | 0.001211865 | 0.004626596 | 0.038151316 | 0.009132335 |
SCA | 0.01342705 | 0.045977858 | 0.222876722 | 0.035254772 |
TSA | 0.002027996 | 0.009666823 | 0.041048048 | 0.012001515 |
HHO | 0.001721616 | 0.013623637 | 0.053045786 | 0.015070571 |
GWO | 0.001428873 | 0.01122106 | 0.044307694 | 0.014886843 |
ChOA | 0.013439016 | 0.140441284 | 0.222883129 | 0.0847737 |
RUN | 0.001024176 | 0.001859894 | 0.002444366 | 0.000471232 |
Method | Min | Mean | Max | STD |
---|---|---|---|---|
INFO | 0.000982755 | 0.001020116 | 0.001375801 | 0.000102525 |
MFO | 0.001330898 | 0.005416622 | 0.03343477 | 0.009512679 |
SCA | 0.020743587 | 0.048102495 | 0.222874404 | 0.033606862 |
TSA | 0.00182302 | 0.005201682 | 0.009756115 | 0.00243312 |
HHO | 0.002601794 | 0.01939235 | 0.075410943 | 0.018505278 |
GWO | 0.001163084 | 0.008847679 | 0.036965034 | 0.011666124 |
ChOA | 0.015533816 | 0.131722062 | 0.222885353 | 0.088246876 |
RUN | 0.000990819 | 0.002047384 | 0.003455065 | 0.000712643 |
Method | Min | Mean | Max | STD |
---|---|---|---|---|
INFO | 0.00098297 | 0.001056164 | 0.001437688 | 0.000146373 |
MFO | 0.000998934 | 0.004563716 | 0.038151316 | 0.00819224 |
SCA | 0.015666298 | 0.042052252 | 0.069572049 | 0.009842541 |
TSA | 0.002159304 | 0.007026558 | 0.037687456 | 0.008747154 |
HHO | 0.002093376 | 0.040618119 | 0.298876672 | 0.073846334 |
GWO | 0.001082604 | 0.009946247 | 0.039243665 | 0.012813202 |
ChOA | 0.011807743 | 0.147804062 | 0.222894455 | 0.082865451 |
RUN | 0.000987658 | 0.002021996 | 0.003785302 | 0.000846304 |
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Hassan, A.Y.; Ismaeel, A.A.K.; Said, M.; Ghoniem, R.M.; Deb, S.; Elsayed, A.G. Evaluation of Weighted Mean of Vectors Algorithm for Identification of Solar Cell Parameters. Processes 2022, 10, 1072. https://doi.org/10.3390/pr10061072
Hassan AY, Ismaeel AAK, Said M, Ghoniem RM, Deb S, Elsayed AG. Evaluation of Weighted Mean of Vectors Algorithm for Identification of Solar Cell Parameters. Processes. 2022; 10(6):1072. https://doi.org/10.3390/pr10061072
Chicago/Turabian StyleHassan, Amir Y., Alaa A. K. Ismaeel, Mokhtar Said, Rania M. Ghoniem, Sanchari Deb, and Abeer Galal Elsayed. 2022. "Evaluation of Weighted Mean of Vectors Algorithm for Identification of Solar Cell Parameters" Processes 10, no. 6: 1072. https://doi.org/10.3390/pr10061072
APA StyleHassan, A. Y., Ismaeel, A. A. K., Said, M., Ghoniem, R. M., Deb, S., & Elsayed, A. G. (2022). Evaluation of Weighted Mean of Vectors Algorithm for Identification of Solar Cell Parameters. Processes, 10(6), 1072. https://doi.org/10.3390/pr10061072