Degradation Cost Analysis of Li-Ion Batteries in the Capacity Market with Different Degradation Models
Abstract
:1. Introduction
2. The Necessity for a Capacity Market
3. Methods
3.1. Problem Setup
- is the de-rated capacity and is the de-rating factor
- and are the CM auction clearing price and the battery degradation cost respectively
- is a factor used to reward slightly more payment in peak demand months
- is the CM overpayment as a result of battery discharging more than its obligation
- is the CM penalty
- is the battery connection capacity which is function of the battery current, voltage and the number of cells ()
- and are the undelivered and over delivered capacity of the obligation during settlement period (i)
- is the capacity lost as a result of battery degradation for model j
- is the peak electricity demand during the SSE () divided by the total CM contracted capacity through the CM auction ()
- Equation (1) calculates the total revenue for a battery in the CM including any overpayment and penalties
- Equation (2) obtain the de-rating capacity based on the battery output power in Equation (3) and the chosen de-rating strategy (i.e., 0.5 h, 1 h etc.)
- Equation (4) calculates the penalty of the battery by multiplying any undelivered capacity obligation by the CM’s auction clearing price. The amount of undelivered capacity is calculated based on the battery’s State of Charge (SoC) at the end of any SSE.
- Equation (5) calculates the overpayment similar to (4)
- Equation (6) calculates the battery capacity degradation cost by multiplying the cell degradation by the cost of degradation along with the number of cells
- Equation (7) calculates the capacity obligation that must be delivered by the battery considering the duration of the SSE(i) and peak demand in Equation (8) minus any delivered balancing services capacity
3.2. Equivalent Circuit Battery Model
3.3. Degradation Models
3.3.1. Empirical Model
3.3.2. Semi-Empirical Model
3.4. Degradation Cost
4. Results
4.1. Accuracy of Battery Degradation Models
4.2. Revenue and Degradation Cost in the Capacity Market
4.2.1. Revenue and Degradation Cost for Different Temperatures
4.2.2. Revenue and Degradation Cost for Different SoCs
4.3. Increased Battery Cycling Effects
5. Discussion
6. Conclusions
Supplementary Materials
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
Appendix A
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Battery Capacity (MWh) | Connection Capacity (MW) | Duration (h) |
---|---|---|
2 | 2 | 0.5 |
2 | 2 | 1 |
2 | 1 | 2 |
2 | 0.5 | 4 |
SoC | OCV (V) | R0 (mΩ) | R1 (mΩ) | C1 (kF) | R2 (mΩ) | C2 (kF) |
---|---|---|---|---|---|---|
0 | 3.5136 | 9.6145 | 4.944 | 9.792 | 0.746 | 27.958 |
0.1 | 3.579 | 9.3483 | 4.928 | 12.621 | 0.572 | 38.512 |
0.2 | 3.623 | 9.5188 | 4.925 | 14.635 | 0.507 | 37.631 |
0.3 | 3.662 | 9.4834 | 4.90 | 15.301 | 0.498 | 26.237 |
0.4 | 3.694 | 9.4206 | 4.878 | 13.912 | 0.270 | 20.286 |
0.5 | 3.727 | 9.3673 | 4.899 | 11.905 | 0.0032 | 18.975 |
0.6 | 3.813 | 9.356 | 4.890 | 14.256 | 0.2385 | 15.288 |
0.7 | 3.899 | 9.3326 | 4.889 | 14.488 | 0.556 | 16 |
0.8 | 3.991 | 9.3847 | 4.884 | 13.775 | 0.288 | 18.763 |
0.9 | 4.092 | 9.240 | 4.822 | 15.166 | 0.659 | 18.454 |
1 | 4.21 | 9.351 | 4.885 | 12.889 | 0.490 | 12.412 |
Degradation Type | Empirical RMSE [%] | Semi-Empirical RMSE [%] |
---|---|---|
Calendar | 3.4 | 4.9 |
Cycle | 1.7 | 1.1 |
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Gailani, A.; Al-Greer, M.; Short, M.; Crosbie, T. Degradation Cost Analysis of Li-Ion Batteries in the Capacity Market with Different Degradation Models. Electronics 2020, 9, 90. https://doi.org/10.3390/electronics9010090
Gailani A, Al-Greer M, Short M, Crosbie T. Degradation Cost Analysis of Li-Ion Batteries in the Capacity Market with Different Degradation Models. Electronics. 2020; 9(1):90. https://doi.org/10.3390/electronics9010090
Chicago/Turabian StyleGailani, Ahmed, Maher Al-Greer, Michael Short, and Tracey Crosbie. 2020. "Degradation Cost Analysis of Li-Ion Batteries in the Capacity Market with Different Degradation Models" Electronics 9, no. 1: 90. https://doi.org/10.3390/electronics9010090
APA StyleGailani, A., Al-Greer, M., Short, M., & Crosbie, T. (2020). Degradation Cost Analysis of Li-Ion Batteries in the Capacity Market with Different Degradation Models. Electronics, 9(1), 90. https://doi.org/10.3390/electronics9010090