Voltage H∞ Control of a Vanadium Redox Flow Battery
Abstract
:1. Introduction
2. System Modeling
2.1. Operation of a VRFB
2.2. VRFB Electrochemical Model
3. Equilibrium Points Analysis
4. Controller Design
4.1. Introduction
4.2. Model Simplification
- Vanadium concentrations are the same on both sides of the half cell. Therefore, it is possible to have the following correspondence:
- The tanks concentration can be expressed in terms of SOC and total vanadium concentration :
4.3. System Linearization
4.4. Uncertainty Modeling
- Determine a frequency range where to model the uncertainty. In our case the, range has been selected. As can be seen in Figure 6, out of this frequency range there is almost no variability in the response. 500 points logarithmically distributed have defined in this range.
- Sample the set of plants, obtained in step 1 and the range of frequencies selected in step 2.
- Compute the error (distance) between each point with respect the nominal plant.
- Obtain stable and minimum phase rational function of polynomials that bounds all of the points obtained in step 4. The rational function order must be selected making a trade-off between the order of the function and the goodness of the fit.
4.5. Controller Design
4.6. Integral Controller Design
4.7. Materials and Methods
5. Results and Discussion
6. Conclusions and Future Work
Author Contributions
Funding
Conflicts of Interest
Abbreviations
ESS | Energy storage systems |
NP | Nominal performance |
OCV | Open circuit voltage |
RES | Renowable energy sources |
RFB | Redox flow battery |
RP | Robust performance |
RS | Robust stability |
SOC | State of charge |
VRFB | Vanadium redox flow battery |
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Parameter | Meaning | Unit—Value |
---|---|---|
Concentration of specie i inside the cell | ||
E | Electrode potential | V |
Standard potential | 1.259 V | |
T | Temperature of the cell | K |
F | Faraday’s constant | 96,485 |
R | Gas constant | 8.314 |
Parameter | Meaning | Unit—Value |
---|---|---|
Volume of the cell | ||
Volume of each tank | ||
Q | Flow rate | |
I | Current | |
S | Surface area of the electrode | 0.15 |
d | Membrane thickness | 1.27·10 |
Diffusion coefficient of | ||
Diffusion coefficient of | ||
Diffusion coefficient of | ||
Diffusion coefficient of | ||
N | Number of cells of the stack | 19 |
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Clemente, A.; Ramos, G.A.; Costa-Castelló, R. Voltage H∞ Control of a Vanadium Redox Flow Battery. Electronics 2020, 9, 1567. https://doi.org/10.3390/electronics9101567
Clemente A, Ramos GA, Costa-Castelló R. Voltage H∞ Control of a Vanadium Redox Flow Battery. Electronics. 2020; 9(10):1567. https://doi.org/10.3390/electronics9101567
Chicago/Turabian StyleClemente, Alejandro, Germán Andrés Ramos, and Ramon Costa-Castelló. 2020. "Voltage H∞ Control of a Vanadium Redox Flow Battery" Electronics 9, no. 10: 1567. https://doi.org/10.3390/electronics9101567
APA StyleClemente, A., Ramos, G. A., & Costa-Castelló, R. (2020). Voltage H∞ Control of a Vanadium Redox Flow Battery. Electronics, 9(10), 1567. https://doi.org/10.3390/electronics9101567