Dynamic Flow Rate Control for Vanadium Redox Flow ... - Science Direct

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ScienceDirect Energy Procedia 105 (2017) 4482 – 4491

The 8th International Conference on Applied Energy – ICAE2016

Dynamic flow rate control for vanadium redox flow batteries Jiahui Fua, Tao Wanga, Xinhao Wanga, Jie Suna, Menglian Zhenga,b,* a

Institute of Thermal Science and Power Systems, College of Energy Engineering, Zhejiang University, Hangzhou, 310027, China b State Key Laboratory of Clean Energy Utilization, Zhejiang University, Hangzhou, 310027, China

Abstract The vanadium redox flow battery (VRB) is one of the most promising technologies for large-scale energy storage. The control of the electrolyte flow rate during its operation has significant impacts on the overall efficiency of the storage system. Although flow-rate optimization under constant current conditions has been addressed in previous studies, few have dealt with varying (dis-)charge power conditions that are common in practice. In this study, an electrochemical model of the VRB has been developed, considering concentration overpotential and the required pump power consumption. The influence of the electrolyte flow rate on the stack efficiency is investigated, and an optimization framework is proposed for determining the optimal flow rate under varying (dis-)charge power conditions. The simulation results demonstrate that the proposed framework could increase the stack efficiency by 3% and limit the electrolyte temperature increment not exceeding 1.4 K. ©©2017 Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license 2016The The Authors. Published by Elsevier Ltd. (http://creativecommons.org/licenses/by-nc-nd/4.0/). Selection and/or peer-review under responsibility of ICAE Peer-review under responsibility of the scientific committee of the 8th International Conference on Applied Energy. Keywords: Vanadium redox flow battery; flow rate control; peak shaving; concentration overpotential; battery management

1. Introduction Flow batteries are considered to be one of the most promising technologies for large-scale energy storage because of their flexible energy and power capacity configurations: The energy and power capacity are independent of each other for flow batteries. In particular, the vanadium redox flow battery (VRB) has been developed and significantly improved over the past decades. A series of models, such as electric models for stacks [1], electrochemical models for unit cells [2, 3], and comprehensive mathematical models [4], have been developed to predict VRB performance under different operating temperatures, current densities, flow rates, etc.

* Corresponding author. Tel.: +86-571-8795-2378; fax: +86-571-8795-2378. E-mail address: [email protected].

1876-6102 © 2017 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of the scientific committee of the 8th International Conference on Applied Energy. doi:10.1016/j.egypro.2017.03.952

Jiahui Fu et al. / Energy Procedia 105 (2017) 4482 – 4491

The electrolyte flow rates could influence the stacks’ heat exchange with the ambience, reactants mass transfer, and pump power consumption. Most previous work was focused on the operation under constant current conditions [5, 6], while few addressed the impacts of the electrolyte flow rate on VRB stacks under varying (dis-)charge power conditions that are common in practice. Such situations include, for example, providing peak-shaving for smoothing demand profiles, where a constant flow rate may lead to a high electrolyte temperature increment under high current densities (i.e., high charge/discharge power) or result in an increased concentration overpotential at low state-of-charge (SoC). Therefore, the results of these previous researches are not directly applicable to VRB operations under varying (dis-)charge power. To provide a method for ensuring continuous operation as well as enhancing the stack efficiency of the VRB system, we herein investigate the electrolyte flow-rate optimization framework under varying (dis)charge power. We first develop an electrochemical model incorporating concentration overpotential and pump power consumption. The model is then run with a specific summer-time peak shaving strategy, and the proposed dynamic optimization framework is utilized to optimize the electrolyte flowrate under the real-time, varying (dis-)charge power specified by the peak shaving strategy. 2. Model development 2.1. General assumptions Several general assumptions are made and adopted throughout this paper (unless otherwise stated): (a) The fluid is treated as impressible and as a dilute solution; (b) The electrode and electrolyte have isotropic and homogeneous physical properties; (c) Isothermal conditions are assumed for all domains; (d) Water permeation, water drag, and side reactions such as the evolution of hydrogen and oxygen and ion crossover are not considered. Besides, it is assumed that all electrolytes are equally distributed through the stack, and all cells have identical performance and are adiabatic with each other. 2.2. Model development All governing equations and corresponding details to describe reaction kinetics, mass balance, and energy balance used in the following parts can be referred to Appendix A. 2.2.1. Reaction kinetics First, Ohm’s Law is used to calculate the voltage (Eq. (3)). Bruggemann’s correction is used to approximate the electrolyte’s effective conductivity as ε3/2σe; for a Nafion® membrane, the empirical correlation is applied to predict the effective conductivity [7, 8] (Eq. (4)). The electrolyte flow rate can greatly influence the surface concentration of the species, and thus, the concentration overpotential and the efficiency of the stack. Here, the concentration overpotential is expressed by the Nernst equation (Eq. (5)). The applied current density is derived with Fick’s Law (Eq. (6)), which describes the diffusion rate between the electrode surface and the electrolyte. The limiting current density is reached when the concentration difference between the electrode and electrolyte reaches the maximum value (Eq. (7)). By combining Eq. (5)−(7) and the correlation obtained from [9], the concentration overpotential at each electrode is then formulated by Eq. (8).

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The activation overpotential is calculated by reversing the Butler−Volmer equation (Eq. (10)) with the charge transfer coefficient D = 0.5 at both electrodes [10]. 2.2.2. Mass balance The mass balance of species in the tank can be expressed by Eq. (11). And the recirculation of electrolytes and electrochemical reactions are calculated by Eq. (12) and (13), respectively. Similarly, the mass balance of the protons in the two electrodes is formulated as Eq. (14) and (15), respectively. 2.2.3. Energy balance The energy balance in this model includes the heat generated by the reaction, ohmic resistance, and overpotentials. It is assumed that the electrolyte entering the electrode could always reach the same temperature with the electrode because of the vast surface area of the porous electrode. Therefore, a general energy balance is achieved (Eq. (16)) with the mass-averaged heat capacity of different components (Eq. (17)). The specific heat capacity of the membrane is estimated by water, as the bulk of the membrane is water-saturated. For the heat source q , the heat capacity may be calculated by taking into account the heat generated by the total overpotentials (Eq. (18) and (19)), reaction (Eq. (20)), and ohmic resistance (Eq. (21)). It is also assumed that the tanks are large enough so that the heat-exchange areas are sufficient to maintain the tanks’ temperatures same as the ambient temperature. Therefore, the electrolyte temperature at the inlets can be set as Tinlet = Tambience. 2.3. Dynamic flow rate optimization framework 2.3.1. Real-time energy efficiency and stack efficiency In this study, we define the energy efficiencies as follows: Ь Real-time energy efficiency Krt (Eq. (22)) denotes the ratio of the power (pump power subtracted) received by appliances to the power discharged from the storage on discharge; it refers to the ratio of the power fed into the storage to the power drawn from the grid (pump power included) on charge. Ь Stack efficiency Kstack (Eq. (23)) denotes the overall ratio of the energy received by appliances to the energy drawn from the grid by the storage over a certain period. The pump power in Eq. (22) and Eq. (23) is related to the pressure drop (associated with the friction and the geometry of hydraulic pipes) and the flow rate. An empirical correlation (Eq. (24)) [13] is used to estimate the pump power consumption under different flow rates. 2.3.2. Flow rate optimization framework The peak-shaving strategy aims to smooth demand profiles by supplementing electricity to appliances at peaks and recharging storage when the grid demand is relatively low (see Fig. 2 (a)). Due to the variations in the appliance power demand, this strategy may cause abrupt changes in the current applied to the VRB stacks. As mentioned, flow rates should be continuously adjusted to adapt to varying (dis)charge current, power, and SoC. The criteria for choosing the optimal flow rate should relate to high energy efficiency, modest increment in the electrolyte temperature, and low concentration overpotential. Based on the Faraday’s Law, flow rates are also associated with the applied current. The relation between the flow rate and


applied current is then formulated (Eq. (25)) with a controllable coefficient fac. This coefficient is then used to adjust the flow rate under varying (dis-)charge power. The flow-rate optimization framework can thus be described as shown in Fig. 1.

Fig. 1. Schematic of the flow-rate optimization framework

3. Results and discussion Simulations are performed with a system comprised of 20 cell stacks (6 kW/6 kWh, 25 unit cells in each stack). Detailed parameters are provided in Appendix B. A 24-h peak-shaving strategy as illustrated in Fig. 1 (a)) is used to produce varying storage (dis-)charge power (details can be found in [14]). 3.1. Impact of flow rate on energy efficiency The strategy is first run to investigate the impacts of different flow rates (range from 0.4 to 20 L/min) on Krt. Fig. 2 (b) and (c) are extracted for 0:00−2:00 and 17:00−19:00 time intervals, respectively. Fig. 2 (b) shows the stack charging process after midnight, where Q = 1.8 L/min results in the highest Krt for charging power below 3 kW (block 1) and Q = 2.4 L/min for power above 3 kW (block 2), indicating that variable flow rates are needed under varying (dis-)charge power. Besides, small flow rates are preferred at small SoCs (in this study, initial SoC = 0.2), while at high SoCs, moderately high flow rates are preferred considering the trade-offs with the increased pump power for increased flow rates. For example, Krt is highest at Q = 2.4 L/min (block 3) though the discharge power is relatively low.

Fig. 2. (a) Schematic of the peak-shaving strategy; (b) Krt under different flow rates from 0:00 to 2:00; (c) Krt under different flow rates from 17:00 to 19:00

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3.2. Optimization results The proposed optimization framework generates a variable flow-rate profile for given varying (dis)charge power generated by the peak-shaving strategy.

Fig. 3. Krt under constant and optimized variable flow rates

Fig. 3 shows the comparison of Krt between the optimized variable flow rates and constant flow rates. The curve for the optimized flow rate not only demonstrates a lasting 0.5% enhancement of Krt for every moment but also maintains Krt above 76.4% for a power profile in the range of 13−3327 W. None of the constant flow rates can resist these vast oscillations of (dis-)charge power, thereby suffering steep efficiency drops from high concentration overpotential under high discharge power (e.g., during 18:00−20:00) or high pump power consumption under relatively small (dis-)charge power (e.g., 22:00).

Fig. 4. (a) Stack efficiency, (b) maximum temperature increment, and (c) maximum concentration overpotential under optimized and constant flow rates

Apart from Krt, as shown in Fig. 4 (b), by adjusting to the flow rate for each (dis-)charge power, the optimization framework demonstrates good thermal control, limiting the maximum temperature difference between the stack (equals the temperature of the electrolyte in the stack) and the ambient temperature to only 1.41 K. From Fig. 4 (c), the maximum concentration overpotential decreases with the increasing flow rate as the concentration gradient in the diffusion layer can be better reduced by the sufficient reactants supply from the electrolytes. Therefore, the optimization helps alleviate the concentration overpotential and maintain an ideal stack output voltage (1.19−1.64V). Besides, Fig. 4 (c) shows a 3% increase of Kstack. This is achieved through the proposed optimization framework, which allows assigning proper flow rates to each (dis-)charge power at varying SoC, thereby saving the power utilized by pump and cutting down the concentration overpotential. 4. Conclusion


An electrolyte flow-rate optimization framework for VRB operating under varying (dis-)charge power is put forward and verified by simulations. With the popularity of VRB for energy storage, this method could provide effective flow-rate optimizations to enhance the performance of VRB stacks under varying (dis-)charge power conditions, and enable the further expansion and application of VRB. Acknowledgements Authors gratefully acknowledge support for the research presented herein from the Fundamental Research Funds for the Central Universities, Grant No. 2016QNA4010. References [1] Barote L, Marinescu C and Georgescu M. VRB modeling for storage in stand-slone wind energy systems. PowerTech,IEEE Bucharest. New York; 2009;1078-83. [2] Shah AA, et al. A dynamic unit cell model for the all-vanadium flow battery. Journal of The Electrochemical Society 2011;158;A671-7. [3] Al-Fetlawi H, Shah AA, Walsh FC. Non-isothermal modelling of the all-vanadium redox flow battery. Electrochimica Acta 2009; 55:1,78-89. [4] Minghua L, Hikihara T. A coupled dynamical model of redox flow battery based on chemical reaction, fluid flow, and electrical circuit. IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences 2007;E91A(7);1741-7. [5] Ma X, Zhang H, Xing F. A three-dimensional model for negative half cell of the vanadium redox flow battery. Electrochimica Acta 2011;58;238-46. [6] Ao T, Jie B, Skyllas-Kazacos M. Studies on pressure losses and flow rate optimization in vanadium redox flow battery. Journal of Power Sources 2014;248;154-62. [7] Springer TE, Zawodzinski TA, Gottesfeld S. Polymer electrolyte fuel cell model. Journal of the Electrochemical Society 1991;138-8;2334-42. [8] Zawodzinski TA, et al. Water uptake by and transport through Nafion ® 117 membranes. Journal of The Electrochemical Society 1993;140-4;1041-47. [9] Schmal D, Van Erkel J, Van Duin PJ. Mass transfer at carbon fibre electrodes. Journal of Applied Electrochemistry 1986;163;422-30. [10] Newman J, Thomas-Alyea KE. Electrochemical Systems. Hoboken: John Wiley & Sons; 2012. [11] Bard AJ, Parsons R, Jordan J. Standard potentials in aqueous solution.Vol 6. Boca Raton: CRC press; 1985. [12] Pourbaix M. Atlas of electrochemical equilibria in aqueous solutions. Houston: National Association of Corrosion Engineers; 1974. [13] Binyu, X, Jiyun Z and Jinbin L. Modeling of an all-vanadium redox flow battery and optimization of flow rates. 2013 IEEE Power & Energy Society General Meeting 2013. [14] Zheng, M, Meinrenken CJ and Lackner KS. Smart households: Dispatch strategies and economic analysis of distributed energy storage for residential peak shaving. Applied Energy, 2015;147;246-257.

Biography Menglian Zheng is an Assistant Professor at the School of Energy Engineering, Zhejiang University, China. Her research interests include flow battery optimization, battery management, and smart energy system.

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Appendix A. Table of equations Equations

E

0 Ecell

0 2

E10

RT § c c c ln ¨ F ¨© cV ( IV ) c( III )

2 V (V ) ( II ) H

· ¸¸ ¹

Description

No.

Nernst Equation

(1)

The proton activity is approximated by cH at the positive electrode.

0 Ecell - ¦ IR - ¦ K

Ecell

k

k

0 ˖open circuit voltage of the unit cell from (1) (V). Ecell

(2)

k

0 Ecell - IR m - IR e - IR c - Ka Kcon , pos Kcon ,neg

IR c

iapp

wc

Vc

ˈ IR m

iapp

wm

Vm

ˈ IR e

iapp

we

H 3 2V e

Ohmic loss of the current collector, membrane and electrolyte

(3)

I : applied current (A) i: applied current density (A/m2)

Vm

§

1 1 º· ¸ ¬ 303 T »¼ ¹

0.5139O - 0.326 exp ¨1268 ª« ©

O: membrane water content( moles of H2O to moles of SO32-), O=22 for the water saturated condition

(4)

T: temperature of the electrode (K)

C RT ln s nF Cbulk

Kcon

n=1

(5)

Cs: reactant concentration at the electrode surface (mol/L) Cbulk: bulk concentration of the electrolyte (mol/L)

i

iL

nFDi

nFDi

Cb

G

Cb - Cs

G

G : thickness of the diffusion layer

(6) 2

Di: diffusion coefficient of species i (m /s)

nFkmCb

iL: the limiting current (A)

(7)

km is the local mass coefficient, and can be approached as

km 1.43 u10-4 u v0.4 [13]

Kcon

· RT § i ¸ ln ¨1nF ¨© 1.43 u10-4 u nF Q / A 0.4 Cb ¸¹

ki

§ nFE 0 i ki ,ref exp ¨ ¨ R ©

ª 1 1 º· - »¸ « ¸ ¬« Ti ,ref T »¼ ¹

Kcon: the concentration overpotential (V)

(8) 2

A: the cross-sectional area of the electrode (m ) Ti,ref =293.15K [14] i=1ˈ2

(9)

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Ka , pos / neg

Positive electrode: cjck = cV(IV)cV(V)

iapp 2 RT a sinh F 2 Fk pos / neg c j ck

(10)

Negative electrode: cjck = cV(II)cV(I) kpos/neg is calculated from (9)

dcitank dt

-

H Ain v Vr

c

tank i

v˖electrolyte inlet velocity at the electrode (m/s)

- ci

tank i

c Ain

(11)

: the concentration of species i in the tank

be we : cross-sectional area of the electrode in the

electrolyte flow direction (m2) Vr

HVe

dci dt

H Ainu citank - ci As

iapp

H Ain u c

iapp

F

(12)

i V II ,V V As

dc HVe i dt

tank i

- ci - As

Negative electrode : HVe

F

dcH dt

i V III ,V IV

H Ainu cHtank - cH +

- Ae - 2 AS

Positive electrode : HVe

UCP cell Vcell

dTcell dt

dcH dt

S: the specific surface area of the electrode (m-1)

(14)

F

(15)

japp F

x

2Q U CP e Ttank T q

HUeCe 1- H UeleCele °

Q : volume flow rate of the electrolyte (m3/s)

UC

x

x

porous electrode

(16) 3

: volume-averaged thermal capacity (J/m ·K)

(17)

membrane current collector

iapp Ka,pos Ka,neg

(18)

iapp Kcon,pos Kcon,neg

(19)

q activation

q con

(13)

iapp

H Ainu cHtan k - cH Ae

SVe : the active surface area for the reaction

p cell

U CP ® UmCm °U C ¯ c c

be we he : volume of the electrode (m3)

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wm we · 2 § wc ¸ iapp ¨ V V Ve ¹ m © c

x

q ohm x

q reaction Krt

iapp

t

³P

storage_to_appliance

0

Ppump

(21)

Ve T 'Spos 'Sneg nF

° Pcharge Pgrid ® °¯ Pappliance Ppump Pdischarge

Kstack t

(20)

dt

charge

Real-time efficiency

(22)

stack efficiency

(23)

Q: electrolyte flow rate (L/min)

(24)

discharge t

³P 0

grid_to_storage

dt

2.74 u102 Q3

Ppump : power consumed by the pump (W) Q

fac u

F c

I

0 reac tan t

0 : the initial concentration of the reactant (mol/L) creactant

u SoC

Appendix B. Default parameters Parameters

Symbols

Values

Reference

Gas constant

R

8.31 J/(mol·K)

Faraday’s constant

F

96485.3 C/mol

N

25

VRB tack parameters Number of cells

0

Initial vanadium concentration (V(II)+V(III), V(IV)+V(V))

c

1.5 mol/L

Initial concentration of protons

cH0

4 mol/L

Half cell volume

Vcell

2.4 u10-4 m3

Tank volume (single)

Vtank

600 L

Porosity of the electrode

e

0.67

S

2 u10 m

Height of the electrode

he

0.3 m

Breadth of the electrode

be

0.2 m

Width of the electrode

we

0.004 m

Width of the membrane

wm

1.25 u10-4 m

Width of the current collector

wc

0.005 m

Ion conductivity of the electrolyte (for both half cells)

Ve

100 S/m

Specific surface area for the reaction

[3] 6

-1

[3]

Geometric default values of the unit cell

[3]

(25)


Electronic conductivities of the current collectors

Vc

9.1h104 S/m

[3]

DV(II)

2.4×10-10 m/s

[4]

Default mass transfer parameters Diffusion coefficient of V(II)

-10

Diffusion coefficient of V(III)

DV(III)

2.4×10

m/s

[4]

Diffusion coefficient of V(IV)

DV(IV)

3.9×10-10 m/s

[4]

Diffusion coefficient of V(V)

-10

DV(V)

3.9×10

m/s

[4]

Reference potential for the reaction at the negative electrode (298.15K)

E10

-0.255 V

[15]

Reference potential for the reaction at the positive electrode (298.15K)

E20

1.004 V

[15]

Standard rate constant of the reaction at the negative electrode (293.15K)

k1,ref

1.44 u10-7 m/s

[4]

Standard rate constant of the reaction at the positive electrode (293.15K)

k2,ref

3.49 u10-7 m/s

[4]

Electrolyte thermal conductivity

Ol

0.67 W/(mgK)

[6]

Electrode thermal conductivity

Oe

0.15 W/(mgK)

[6]

Membrane thermal conductivity

Om

0.67 W/(mgK)

[6]

Current collector thermal conductivity

Oc

16 W/(mgK)

[6]

Water thermal capacitance

UlCl

4.187×10 J/(m3·K)

[6]

Electrode thermal capacitance

UeCe

3.33×106 J/(m3·K)

[6]

Membrane thermal capacitance

UmCm

2.18×106 J/(m3·K)

[6]

Current collector thermal capacitance

UcCc

4.03×106 J/(m3·K)

[6]

Entropy of the reaction at the negative electrode

-'S1

-100 J/(mol·K)

[16]

Entropy of the reaction at the positive electrode

-'S 2

-21.7J/(mol·K)

[16]

Default electrochemistry parameters

Default thermal properties

6

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