Modelling, Parameter Identification, and Experimental Validation of a Lead Acid Battery Bank Using Evolutionary Algorithms
Abstract
:1. Introduction
2. Battery Model Test
3. Parameter Identification
3.1. EAs’ Descriptions
3.2. New Proposal
3.3. Algorithms Configuration Criteria
4. Results and Discussion
4.1. Optimization Results
4.2. Model Performance and Validation
4.3. Experimental Validation
5. Conclusions
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
References
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Parameters | Guasch [39] | Copetti [40] | Blaifi [41,42] | Blaifi [43] |
---|---|---|---|---|
Vbodc (V) | 2.147 | 2.085 | 2.148 | 2.1612 |
Kbodc (V) | 0.284 | 0.12 | 0.127 | 0.219 |
P1dc (VAh) | 4.083 | 4 | 0.406 | 9.5044 |
P2dc | −6.634 | 1.3 | 3.041 | 4.9361 |
P3dc (Vh) | 0.27 | 0.27 | 1.218 | 0.9311 |
P4dc | 1.5 | 1.5 | 0.7812 | 0.037 |
P5dc (Vh) | 0.02 | 0.02 | 0.484 | 1.8837 |
αrdc (°C−1) | 0.007 | 0.007 | 0.0197 | 0.0167 |
Vboc (V) | 1.98 | 2 | 1.781 | 1.9016 |
Kboc (V) | 0.149 | 0.16 | 0.5313 | 0.16 |
P1c (VAh) | 5.923 | 6 | 7.234 | 6.0809 |
P2c | 0.024 | 0.86 | 0.667 | 1.6701 |
P3c (Vh) | 0.48 | 0.48 | 0.078 | 0.3375 |
P4c | 1.2 | 1.2 | 0.492 | 0.9853 |
P5c (Vh) | 0.036 | 0.036 | 0.7421 | 1.7838 |
αrc (°C−1) | 0.025 | 0.025 | 0.43 | 0.01 |
Criteria | PSO | PSO + P | CS |
---|---|---|---|
Population size | 1000 | 1000 | 1000 |
Iterations | 100 | 100 | 100 |
Weight initial (ω1) | 0.9 | 0.9 | - |
Weight final (ω2) | 0.1 | 0.1 | - |
c1 | 1 | 1 | - |
c2 | 1 | 1 | - |
vd | 5 | 5 | 5 |
Iteration to perturb | - | 10 | - |
Pa | - | - | 0.5 |
α | - | - | 1 |
λ | - | - | 2 |
Criteria/Algorithm | PSO | PSO + P | Cuckoo | ||||
---|---|---|---|---|---|---|---|
d * | c * | d * | c * | d * | c * | ||
Precision (error) | Value | 0.50 | 0.91 | 0.34 | 0.51 | 3.09 | 2.81 |
Score | 1.48 | 1.78 | 1.00 | 1.00 | 9.23 | 5.53 | |
Velocity (iteration) | Value | 17.00 | 11.00 | 91.00 | 90.00 | 89.00 | 97.00 |
Score | 1.00 | 1.00 | 5.35 | 8.18 | 5.24 | 8.82 | |
Computational cost (ms/iteration) | Value | 0.41 | 0.41 | 0.42 | 0.42 | 0.71 | 0.71 |
Score | 1.00 | 1.00 | 1.03 | 1.03 | 1.72 | 1.72 |
Discharge | Charge | ||
---|---|---|---|
Vbodc (V) | 2.3003 | Vboc (V) | 2.2823 |
Kbodc (V) | 0.1898 | Kboc (V) | 1.0227 |
P1dc (VAh) | 20.4751 | P1c (VAh) | 2.4048 |
P2dc | 0.9282 | P2c | 1.1928 |
P3dc (Vh) | 0.1481 | P3c (Vh) | 0.0061 |
P4dc | 2.3350 | P4c | 0.0285 |
P5dc (Vh) | 0.0362 | P5c (Vh) | 0.0054 |
αrdc (°C−1) | 0.0365 | αrc (°C−1) | 0.1008 |
kIdc * | 2.2087 | kIc * | 0.3254 |
kc_batdc * | 2.5517 | kc_batc * | 0.3603 |
ksocdc * | 2.5509 | ksocc * | 16.7918 |
kc120dc * | 0.0470 | kc120c * | 0.3097 |
Signal | SOC | Voltage | ||||
---|---|---|---|---|---|---|
Month | (1) | (2) | (3) | (1) | (2) | (3) |
Charge mode error (%) | 0.0606 | 0.0827 | 0.1787 | 0.2163 | 0.2504 | 0.2446 |
Discharge mode error (%) | 0.1223 | 0.1335 | 0.1383 | 0.3824 | 0.3347 | 0.5242 |
Mean (%) | 0.0956 | 0.1076 | 0.1602 | 0.3075 | 0.2904 | 0.3582 |
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Ariza Chacón, H.E.; Banguero, E.; Correcher, A.; Pérez-Navarro, Á.; Morant, F. Modelling, Parameter Identification, and Experimental Validation of a Lead Acid Battery Bank Using Evolutionary Algorithms. Energies 2018, 11, 2361. https://doi.org/10.3390/en11092361
Ariza Chacón HE, Banguero E, Correcher A, Pérez-Navarro Á, Morant F. Modelling, Parameter Identification, and Experimental Validation of a Lead Acid Battery Bank Using Evolutionary Algorithms. Energies. 2018; 11(9):2361. https://doi.org/10.3390/en11092361
Chicago/Turabian StyleAriza Chacón, H. Eduardo, Edison Banguero, Antonio Correcher, Ángel Pérez-Navarro, and Francisco Morant. 2018. "Modelling, Parameter Identification, and Experimental Validation of a Lead Acid Battery Bank Using Evolutionary Algorithms" Energies 11, no. 9: 2361. https://doi.org/10.3390/en11092361