Thermal Modeling of Vanadium Redox Flow Battery
Student: Jia Junduo
Supervisor: Asst Prof Zhao Jiyun
Co-Supervisor: Mr. Ng Kian Wee
Examiner: Assoc Prof Ali I. Maswood
1. Introduction
Tank
Catholyte
Tank
Anolyte
PUMP PUMP
Cation Exchange Membrane
ELECTR
OD
E
ELECTR
OD
E Cell
STACK
1. Introduction
elec
tro
de
elec
tro
de
dis
char
ge
dis
char
ge
char
ge
char
ge
reduction
reduction
oxidation
oxidation
Load
mem
bra
ne
1. Introduction
Positive: 𝑉𝑂 + 2𝐻 + 𝑒 ↔ 𝑉𝑂 +
𝐻 𝑂
Negative: 𝑉 ↔ 𝑉 + 𝑒
The overall equation is:
𝑉 + 𝑉𝑂 + 2𝐻 ↔ 𝑉𝑂 + 𝑉 +
𝐻 𝑂
1. Introduction
Objective: Construct a thermal model
Influencing factors: Flow rate, currents and surrounding temperature vs Stack/Tank temperature
2. Literature Review
W.Skyllas-Kazacos, C.Menictas, M.Kazacos, J Electrochem Soc, 143 (1996) LB6-L88
In the negative half-cell, the V(2+) and V(3+) ions will start to precipitate at a temperature lower than about 10 degree Celsius. For V(4+) and V(5+) ions in the positive half-cell, they will start to precipitate at a temperature above about 50 degree Celsius.
2. Literature Review A.Tang, S.M.Ting, J. Bao, M.Skyllas-Kazacos, J Power Sources, 203 (2012) 165-176
𝐶𝑝𝜌𝑉𝑠𝑑𝑇𝑠
𝑑𝑡= 𝑄 𝐶𝑝𝜌 𝑇𝑡+ − 𝑇𝑠 + 𝑄 𝐶𝑝𝜌 𝑇𝑡− − 𝑇𝑠 +
𝑈𝑠𝐴𝑠 𝑇𝑎𝑖𝑟 − 𝑇𝑠 + 𝐼 𝑅
𝐶𝑝𝜌𝑉𝑡 𝑑𝑇𝑡+
𝑑𝑡= 𝑄 𝐶𝑝𝜌 𝑇𝑠 − 𝑇𝑡 + 𝑈 𝐴𝑡 𝑇𝑎𝑖𝑟 − 𝑇𝑡
𝐶𝑝𝜌𝑉𝑡 𝑑𝑇𝑡−
𝑑𝑡= 𝑄 𝐶𝑝𝜌 𝑇𝑠 − 𝑇𝑡 + 𝑈 𝐴𝑡 𝑇𝑎𝑖𝑟 − 𝑇𝑡
3. Methodology
𝐶𝑝𝜌𝑉𝑠𝑑𝑇𝑠
𝑑𝑡= 𝑄 𝐶𝑝𝜌 𝑇𝑡+ − 𝑇𝑠 +
𝑄 𝐶𝑝𝜌 𝑇𝑡− − 𝑇𝑠 + 𝑈𝑠𝐴𝑠 𝑇𝑎𝑖𝑟 − 𝑇𝑠 +
𝑃𝑅 + 𝑃𝑐ℎ
𝐶𝑝𝜌𝑉𝑡 𝑑𝑇𝑡+
𝑑𝑡= 𝑄 𝐶𝑝𝜌 𝑇𝑠 − 𝑇𝑡 +
𝑈 𝐴𝑡 𝑇𝑎𝑖𝑟 − 𝑇𝑡 + 𝑃𝑝𝑢𝑚𝑝
𝐶𝑝𝜌𝑉𝑡 𝑑𝑇𝑡−
𝑑𝑡= 𝑄 𝐶𝑝𝜌 𝑇𝑠 − 𝑇𝑡 +
𝑈 𝐴𝑡 𝑇𝑎𝑖𝑟 − 𝑇𝑡 + 𝑃𝑝𝑢𝑚𝑝
3.1 power losses due to the internal resistance
𝑃𝑅 = 𝐼 𝑅
Charging or Discharging: Different currents and internal resistance
3.2 Chemical Power Loss
q = T∆S = T 𝑆𝑝𝑟𝑜𝑑𝑢𝑐𝑡𝑠 − 𝑆𝑟𝑒𝑎𝑐𝑡𝑎𝑛𝑡𝑠
𝑃𝑐ℎ = 𝑞𝑛 = 𝑇∆𝑆𝑛
C.Blanc, Modeling of a vanadium redox flow battery electricity storage system, Phd thesis, Ecole polytech Fed Lausanne, 2009.
3.3 Pump Power Loss
Friction loss
Form loss
𝑃𝑝𝑢𝑚𝑝 = ∆𝑝 × 𝑄
∆p = ∆𝑝𝑓𝑟𝑖𝑐𝑡𝑖𝑜𝑛 + ∆𝑝𝑓𝑜𝑟𝑚
∆𝑝𝑓𝑟𝑖𝑐𝑡𝑖𝑜𝑛 = 𝑓𝐿
𝐷ℎ
𝜌𝑉𝑚2
∆𝑝𝑓𝑜𝑟𝑚 = 𝐾𝜌𝑉𝑚
2
3.3 Pump Power Loss
2 parts: Stack and Hydraulic Structure
To calculate friction loss in stack:
3.4 State Space Model
𝑥 = 𝐴𝑥 + 𝐵𝑢
y = Cx + Du
𝑑𝑇𝑠
𝑑𝑡= −
𝑄+ 𝑄−
𝑉𝑠−
𝑈𝑠𝐴𝑠
𝐶𝑝𝜌𝑉𝑠𝑇𝑠 +
𝑄+
𝑉𝑠𝑇𝑡 +
𝑄−
𝑉𝑠𝑇𝑡 +
𝑈𝑠𝐴𝑠
𝐶𝑝𝜌𝑉𝑠𝑇𝑎𝑖𝑟 +
1
𝐶𝑝𝜌𝑉𝑠𝑃𝑅 +
1
𝐶𝑝𝜌𝑉𝑠𝑃𝑐ℎ
𝑑𝑇𝑡+
𝑑𝑡=
𝑄+
𝑉𝑡+𝑇𝑠 + −
𝑄+
𝑉𝑡+−
𝑈+𝐴𝑡
𝐶𝑝𝜌𝑉𝑡+𝑇𝑡 +
𝑈+𝐴𝑡
𝐶𝑝𝜌𝑉𝑡+𝑇𝑎𝑖𝑟 +
1
𝐶𝑝𝜌𝑉𝑡+𝑃𝑝𝑢𝑚𝑝
𝑑𝑇𝑡−
𝑑𝑡=
𝑄−
𝑉𝑡−𝑇𝑠 + −
𝑄−
𝑉𝑡−−
𝑈−𝐴𝑡
𝐶𝑝𝜌𝑉𝑡−𝑇𝑡 +
𝑈−𝐴𝑡
𝐶𝑝𝜌𝑉𝑡−𝑇𝑎𝑖𝑟 +
1
𝐶𝑝𝜌𝑉𝑡−𝑃𝑝𝑢𝑚𝑝
3.4 State Space Model
The state vector x =
𝑇𝑠𝑇𝑡 𝑇𝑡
, input u =
𝑃𝑅𝑇𝑎𝑖𝑟𝑃𝑝𝑢𝑚𝑝𝑃𝑐ℎ
A =
−𝑄+ 𝑄−
𝑉𝑠−
𝑈𝑠𝐴𝑠
𝐶𝑝𝜌𝑉𝑠
𝑄+
𝑉𝑠
𝑄−
𝑉𝑠
𝑄+
𝑉𝑡+−
𝑄+
𝑉𝑡+−
𝑈+𝐴𝑡
𝐶𝑝𝜌𝑉𝑡+0
𝑄−
𝑉𝑡−0 −
𝑄−
𝑉𝑡−−
𝑈−𝐴𝑡
𝐶𝑝𝜌𝑉𝑡−
B =
1
𝐶𝑝𝜌𝑉𝑠
𝑈𝑠𝐴𝑠
𝐶𝑝𝜌𝑉𝑠0
1
𝐶𝑝𝜌𝑉𝑠
0𝑈+𝐴𝑡
𝐶𝑝𝜌𝑉𝑡+
1
𝐶𝑝𝜌𝑉𝑡+0
0𝑈−𝐴𝑡
𝐶𝑝𝜌𝑉𝑡−
1
𝐶𝑝𝜌𝑉𝑡−0
C =1 0 00 1 00 0 1
D = 0
4. Simulations and Results
MATLAB is used to perform the simulation
4.1 Chemical power loss and power loss due to internal resistance
4.2 Pump power loss
4.3 Simulations of stack temperature with various flow rate
(𝐼𝑐ℎ𝑎𝑟𝑔𝑖𝑛𝑔 = 𝐼𝑑𝑖𝑠𝑐ℎ𝑎𝑟𝑔𝑖𝑛𝑔 = 30𝐴, surrounding temperature
25 constant)
𝑄 = 30𝑐𝑚 𝑠 1
𝑄 = 60𝑐𝑚 𝑠 1
𝑄 = 120𝑐𝑚 𝑠 1
𝑄 = 180𝑐𝑚 𝑠 1
𝑄 = 240𝑐𝑚 𝑠 1
4.4 Simulation of stack temperature with various flow rate
(𝐼𝑐ℎ𝑎𝑟𝑔𝑖𝑛𝑔 = 30𝐴, 𝐼𝑑𝑖𝑠𝑐ℎ𝑎𝑟𝑔𝑖𝑛𝑔 = 100𝐴, surrounding
air temperature 25 constant)
𝑄 = 30𝑐𝑚 𝑠 1
𝑄 = 60𝑐𝑚 𝑠 1
𝑄 = 120𝑐𝑚 𝑠 1
𝑄 = 180𝑐𝑚 𝑠 1
𝑄 = 240𝑐𝑚 𝑠 1
4.5 Simulations of stack temperature with various charging and discharging currents
(𝑄𝑠𝑡𝑎𝑐𝑘 = 4 × 𝑄𝑚𝑖𝑛, surrounding air temperature 25 constant)
I=40A
I=60A
I=80A
I=100A
I=120A
4.6 Simulations of stack temperature with changing flow rate
(I=30A, surrounding air are varying between 15℃ to 35℃)
𝑄 = 30𝑐𝑚 𝑠 1
𝑄 = 60𝑐𝑚 𝑠 1
𝑄 = 120𝑐𝑚 𝑠 1
𝑄 = 180𝑐𝑚 𝑠 1
𝑄 = 240𝑐𝑚 𝑠 1
4.7 Simulations of stack temperature with various charging/discharging current (𝑄 = 120𝑐𝑚 𝑠 1, surrounding air are varying between 15℃ to 35℃)
I=80A
I=100A
I=120A
4.8 Simulation of stack temperature and tank temperature I=30A, 𝑄 = 120𝑐𝑚 𝑠 1 and constant surrounding air temperature.
5. Future improvement
Self-discharging and the side reactions will also contribute to heat generation so that the temperature of stack will increase more. Especially, when the battery is standing by, the self-discharging characteristic has to be investigated.
6. Conclusion
a dynamic thermal model based on conservation of energy is developed
friction power loss and form power loss are not negligible
chemical power and internal resistance loss
Factors: flow rate of electrolyte, currents and surrounding air temperature
Acknowledgement
Q&A