Battery modelling and Supercapacitor
sizing for effective retrofitting of BESS
Sandro Masaki, PhD Candidate
1.
Battery model investigation
2.
Optimization model for supercapacitor sizing in BESS
retrofitting application
Battery model investigation
Experiment description
1. Objective: Investigate a lithium battery model with good trade-off between accuracy
and running time.
2. Methodology:
(1) Battery cell charging: CCCV @ 0.5C
(2) Battery relaxation: resting for ± 3 hours
(3) Battery discharge: UDDS current profile with |I|max = 1C or 0.95C
(4) Parameter estimation: experiment data from UDDS with |I|max = 1C
(5) Model validation and performance assessment: experiment data from UDDS
with |I|max = 0.95C
Experiment setup
UDDS cycle @ 1C (Samsung INR18650-29E)
Rint model
𝑁
Estimation Imax @1C
2
Error: ෍ 𝑉𝑖 − 𝑉෠𝑖 = 27.6987
𝑖=1
𝑁
Validation Imax @ 0.95C
Error: ෍ 𝑉𝑖 − 𝑉෠𝑖
𝑖=1
2
= 25.0267 | Sim time: 0.0355 sec
Thevenin ECM
𝑁
Error: ෍ 𝑉𝑖 − 𝑉෠𝑖
Estimation Imax @1C
2
= 0.1948
𝑖=1
𝑁
Validation Imax @ 0.95C
Error: ෍ 𝑉𝑖 − 𝑉෠𝑖
𝑖=1
2
= 0.2284 | Sim time: 0.0375 sec
Double-Capacitor ECM
𝑁
2
Error: ෍ 𝑉𝑖 − 𝑉෠𝑖 = 0.1752
Estimation Imax @1C
𝑖=1
𝑁
Validation Imax @ 0.95C
2
Error: ෍ 𝑉𝑖 − 𝑉෠𝑖 = 0.142 | Sim time: 0.0389 sec
𝑖=1
Nonlinear Double-Capacitor ECM (N. Tian et al., 2021)
𝑁
2
Error: ෍ 𝑉𝑖 − 𝑉෠𝑖 = 0.0168
Estimation Imax @1C
𝑖=1
Validation Imax @ 0.95C
𝑁
Error: ෍ 𝑉𝑖 − 𝑉෠𝑖
𝑖=1
2
= 0.0206 | Sim time: 2.17 sec
Proposed ECM #1
𝑁
Error: ෍ 𝑉𝑖 − 𝑉෠𝑖
Estimation Imax @1C
2
= 0.1421
𝑖=1
𝑁
Error: ෍ 𝑉𝑖 − 𝑉෠𝑖
Validation Imax @ 0.95C
𝑖=1
2
= 0.1123| Sim time: 0.0682 sec
Performance comparison
Estimation
error
Validation error
Average time
(sec.)
Rint model
27.6987 (5)
25.0267
0.0355 (1)
Thevenin ECM
0.1948 (4)
0.2284
0.0375 (2)
Double-Capacitor ECM
0.1752 (3)
0.1383
0.0389 (3)
Nonlinear Double-Capacitor ECM
0.0168 (1)
0.0206
2.3433 (5)
Proposed ECM #1
0.1421 (2)
0.1123
0.0682 (4)
Model
Optimization model for supercapacitor sizing
in BESS retrofitting application
Research Gap
General observations from literature study: In battery-supercapacitor
HESS, supercapacitor is typically sized to either:
- Reduce current fluctuations on the battery;
- Minimize the capital cost of HESS;
- Minimize the total weight of HESS (PHEV, EV).
None of this sizing method is suitable in the case of stationary BESS retrofit
with supercapacitor. The objective should be to minimize the life cycle cost
of the new battery-supercapacitor HESS.
Supercapacitor sizing
Optimization Problem
min 𝐿𝐶𝐶 = 𝐽(𝐶𝑆𝐶 , 𝐼𝑏𝑎𝑡,1 , … 𝐼𝑏𝑎𝑡,𝑁 , 𝐼𝑠𝑐,1 , … , 𝐼𝑠𝑐,1 )
subject to
𝐼𝑏𝑎𝑡 𝑘 + 𝐼𝑠𝑐 𝑘 = 𝐼ℎ𝑒𝑠𝑠 𝑘
𝑉𝑏𝑎𝑡,𝑚𝑖𝑛 ≤ 𝑉𝑏𝑎𝑡 (𝑘) ≤ 𝑉𝑏𝑎𝑡,𝑚𝑎𝑥
𝑉𝑆𝐶,𝑚𝑖𝑛 ≤ 𝑉𝑆𝐶 𝑘 ≤ 𝑉𝑆𝐶,𝑚𝑎𝑥
𝑄𝑏𝑎𝑡𝑡,𝑛𝑜𝑚 − 𝑄𝑏𝑎𝑡𝑡,𝐸𝑂𝐿
𝑁−1≤
≤𝑁
𝑄𝑏𝑎𝑡𝑡,𝑙𝑜𝑠𝑠
λ ∗ 𝑁 − 1 ≤ 𝐿𝑆𝐶 ≤ λ ∗ 𝑁
Optimization Problem
Where
𝐽 = 𝐶𝐶𝑆𝐶 + 𝐶𝐶𝑐𝑜𝑛𝑣 + 𝑂𝐶𝑙𝑜𝑠𝑠 + 𝑂𝐶𝐻𝑉𝐴𝐶
𝑉𝑏𝑎𝑡 𝑘 = ℂ𝑏𝑎𝑡 ∗ 𝑉𝑏𝑎𝑡 𝑘 + 𝔻𝑏𝑎𝑡 ∗ 𝐼𝑏𝑎𝑡 𝑘
𝑉𝑆𝐶 𝑘 = ℂ𝑆𝐶 ∗ 𝑉𝑆𝐶 𝑘 + 𝔻𝑆𝐶 ∗ 𝐼𝑆𝐶 𝑘
𝑄𝑏𝑎𝑡𝑡,𝑙𝑜𝑠𝑠 = 𝑓 𝐼𝑏𝑎𝑡,1 , … 𝐼𝑏𝑎𝑡,𝑁 , 𝑇𝑏𝑎𝑡,1 , … 𝑇𝑏𝑎𝑡,𝑁 , 𝑆𝑜𝐶𝑏𝑎𝑡,1 , … 𝑆𝑜𝐶𝑏𝑎𝑡,𝑁
𝐿𝑆𝐶 = 𝑔(𝐼𝑠𝑐,1 , … , 𝐼𝑠𝑐,𝑁 , 𝑉𝑠𝑐,1 , … , 𝑉𝑠𝑐,𝑁 )
THANK YOU FOR YOUR ATTENTION!