Printer Friendly

Estimating the state-of-charge of all-vanadium redox flow battery using a divided, open-circuit potentiometric cell.

I. INTRODUCTION

Current economic developments demand stability in energy security for future accessibility [1]. Redox flow battery (RFB), developed in the 1970s [2] and shares similar principles as fuel cells, is a rechargeable battery that uses flowing redox species that flow through cell stack to convert chemical energy into electricity. RFB has the ability to decouple its power component from the energy components. Its modular nature presents it as a viable option for use in many applications, such as uninterrupted power supply, load levelling and stand-alone applications [3].

An all-vanadium redox flow battery (V-RFB) is one of the electrochemical energy storage systems that is suitable for many applications due to its high energy efficiency (>80%) [4], [5]. Fig. 1 depicts the principles of operation of a V-RFB. The overall cell reaction is as follows:

[V.sup.3+] + V[O.sup.2+] + [H.sub.2] [left right arrow] V[O.sub.2.sup.+] + 2[H.sup.+] + [V.sup.2+], (1)

[E.sup.o] = 1.26V vs. SHE. (2)

Theoretically, V-RFB does not suffer from capacity degradation as the same electrolyte species is used in both the positive and negative reservoirs. Also, V-RFB can be over-discharged without causing significant harm to the battery [6], [7]; the batteries could be cycled at lower state of-charge (SOC) (20 % to 80 % SOC) [8].

However, overcharging the V-RFB should be avoided as it could have detrimental effects on the electrolyte and the cell components. Noack et al. [8] stated that overcharging beyond a certain voltage level would result in electrolysis of water into hydrogen on the negative electrode and oxygen at the positive electrode. Also, Mohammadi et al. stated that overcharging would increase the cell's resistance [9], which results in capacity loss of the battery [10].

Due to various cell reactions, as discussed in numerous literatures [9]-[13], estimation of SOC is best done at the reference cell instead of within the cell stack. The oxidation-reduction potential (ORP) method can be used, where the maximum point of redox could be related to the open-circuit voltage (OCV) of the V-RFB. Since OCV is a function of SOC [14], the accuracy of the battery's SOC is dependent on the accurate estimation of the OCV.

In this paper, potentiometric measurement is used for estimating kinetic parameters and current efficiency for electrolyte batches of V(IV)/V(V) and V(III)/V(II) to achieve its equilibrium state, and subsequently, V-RFB's SOC could be estimated. Also, continuous monitoring of the potential difference between two working electrodes and two half-cell potentials against Hg/[Hg.sub.2]S[O.sub.4] reference electrodes is discussed.

II. METHODOLOGY ESTABLISHMENT

Sharkh et al. [15] noted that to establish the state-of-health (SOH) of a battery, correct estimation of SOC is essential. Besides, precise knowledge of SOC will facilitate optimal operation of a battery with minimal degradation effects, hence increasing the life cycle of the battery. Walsh [16] suggested that the details of the cell's equilibrium potential could be used to describe the thermodynamics of the electrochemical system.

The characteristics and parameters of well-known batteries are readily available from the manufactures; one is able to correctly estimate the SOC so as not to overcharge the battery. However, predicting the correct SOC for a newly developed battery, such as the V-RFB, could be difficult, especially for those who are trying to characterise the battery.

Numerous conventional methods, such as direct measurement, specific gravity measurement and current-based estimation (coulomb-counting), can be used to estimate and monitor SOC. However, open-circuit voltage (OCV) method results in very accurate estimation of the SOC but it needs a rest time and cannot be used in real-time [17]. Hence, in this study, OCV approach is adopted due to its suitability for current-controlled environment [18]. By definition, the open-circuit voltage is the voltage of the battery when no current is flowing in or out of the battery since the battery is in a state of equilibrium [14], and in this state the battery reaches 100 % SOC [19].

Oxidation--reduction potential (ORP), widely used in laboratory studies and industrial applications [20], can be used to monitor the concentration of redox species and is related to OCV as the points where oxidation and reduction are in a state of equilibrium. Using potentiometric measurement, the potential difference between the working electrodes and the reference electrodes is compared. The basis of which is the use of Nernst equation to describe the concentration of redox species in terms of the potential at the cell's electrode under equilibrium condition.

III. THEORETICAL EXPRESSION

Trinidad et al. [21] has applied the Nernst equation, mass balance equation of redox reaction and Faraday's law of electrolysis to establish the relationship between the half-cell redox concentration of Ce(IV)/Ce(III) and the ORP during electrolysis. In this study, the approach is extended to monitor both half-cells of redox couple, hence making estimation of SOC possible.

For determining [E.sup.o.sub.cell], Blanc [22] suggested the use of thermodynamic characteristics of the elements involved in V-RFB reactions with [E.sup.o.sub.cell] of 1.23 V, or the combination of two half-cell standard electrode potential with [E.sup.o.sub.cell] of 1.255 V, where the latter value is also suggested by another researcher [8]. However, in this study, [E.sup.o.sub.cell] of 1.26 V is chosen as the standard cell potential as this value is acknowledged by many researchers [7], [23]-[26].

Reaction (1) represents the kinetic reactions of vanadium species in the reversible cell reaction. Eq. (3) represents Nernst equation for determining [E.sub.cell(ORP)]

[E.sub.cell(ORP)] = 1.26 + 0.05916 [log.sub.10] [[C.sub.V(IV)][C.sub.V(II)]/[C.sub.V(V)][C.sub.V(III)]]. (3)

The concentration parameters of the species, [C.sub.red] and [C.sub.oxd], can be determined using Faraday's law of electrolysis. The law describes the amount of substance undergoing an electrochemical change in a constant volume reaction [21]. With constant current and duration for electrolysis, the concentration of a redox species could be determined using (4)[16], [21]. For simplicity, only the reduction process is considered, and the same principle applies to the oxidation process

[([C.sub.red]).sub.t] = [phi]It/zFV. (4)

In the case of mass transport control reaction, the current efficiency varies with time and since there is no co-exist species in the electrolyte during electrolysis, mass balance equation for oxidised species is given by (5)

[([C.sub.oxd]).sub.t] = [([C.sub.oxd]).sub.o]-[([C.sub.red]).sub.t]. (5)

Substituting (4) into (5), the expression of oxidised species at time t is given by (6)

[([C.sub.oxd]).sub.t] = [([C.sub.oxd]).sub.o]-[phi]It/zFV. (6)

For example, if V(V) is the oxidised species, then

[([C.sub.V(V)]).sub.t] = [([C.sub.V(V)]).sub.o]-[phi]It/zFV. (7)

Substituting (6) into (1) and (2), the Nernst equation for V-RFB becomes

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. (8)

Rearranging the (8) in the form of (3), the open-circuit cell potential is as follows

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. (9)

IV. EXPERIMENTAL DETAILS

The experiments were carried out at the Electrochemical Engineering Laboratory, University of Southampton, UK. The redox couples in V-RFB are all soluble species [7] supplied by Re-Fuel Technology Ltd. with the initial concentration of 1.6 mol [dm.sup.-3] of V(III)/V(IV) in 4 mol [dm.sup.-3] [H.sub.2]S[O.sub.4].

Fig. 2 illustrates the system in general of a 25-100 [cm.sup.2] unit cell laboratory unit V-RFB system with concentration flow-tubes, electrical connections, and nitrogen flow.

The experiment is carried out using two systems: the first is based on a 100 [cm.sup.2] unit cell laboratory V-RFB attached to a pair of reference electrodes, and the second is based on a 25 [cm.sup.2] unit cell laboratory unit V-RFB attached to a combination of reference and working electrodes as shown in Fig. 3. The 100 [cm.sup.2] unit cell-reference electrodes based system is used at the beginning of the study as it is capable of generalising the V-RFB system. Meanwhile, the 25 [cm.sup.2] unit cell laboratory units V-RFB is an extension of the initial cell with modification for potentiometric measurement of vanadium species at the reference cell. Details of both experimental setups has been detailed in paper [13].

The main frame compartments of each half of the reference cell consist of 5 cm x 5 cm x 2 cm polyvinyl chloride polymer, separated by an ion exchange membrane. An opening of 1.5 cm x 1.5 cm is made in the centre of the half-cell frame to allow the vanadium electrolyte flow-through and contact between the reference and working electrodes. The reference cell is connected to 25 [cm.sup.2] V-RFB unit as illustrated in Fig. 2. Temperature is maintained at 298 [+ or -] 2 K throughout the experiment and is monitored using thermocouples.

V. RESULTS AND DISCUSSIONS

A. Estimation of electrolytes concentration

The redox potential of V-RFB unit cell has been estimated and plotted using the (10). Prior to the generation of the concentration of the redox species, the following assumptions were made:

Positive electrode

[C.sub.V(IV)] = 0.01 [C.sub.V(V)]. (10)

Negative electrode

[C.sub.V(II)] = 0.01 [C.sub.V(III)]. (11)

Both half-cell reservoirs of the V-RFB system use the same electrolyte, therefore both half-cells should contained a mixture of 50 % V(III) and 50 % V(IV) in [H.sub.2]S[O.sub.4]. Consequently, since the supplied electrolyte is 1.6 mol [dm.sup.-3] V(III)/V(IV) in 4 mol [dm.sup.-3] [H.sub.2]S[O.sub.4], the electrolytes in both half-cells would undergo a formation charge process at the start of experiment. In the process, two mixtures of vanadium species is converted into a single electro-active species of V(III) at negative electrode and V(IV) at positive electrode. At the end of the formation charge process, the positive reservoir should contain 0.8 mol [dm.sup.-3] V(IV) in 4 mol [dm.sup.-3] [H.sub.2]S[O.sub.4], whereas negative reservoir should contain 0.8 mol [dm.sup.-3] V(III) in 4 mol dm 3 [H.sub.2]S[O.sub.4].

In this approach, the concentration of reactants V(IV) and V(III) were assumed to start at very high value and decreases exponentially over time, but the concentration of products V(V) and V(II) increases inversely at the same rate as the reduction of the reactants. Fig. 4 illustrates the changes of concentration for reactant species against product over time.

Based on the assumptions made in (10) and (11), it was established that the estimated initial [E.sub.cell(ORP)] in (9) for 1.6 mol [dm.sup.-3] V(III)/V(IV) in 4 mol [dm.sup.-3] [H.sub.2]S[O.sub.4] using the Nernst equation starts at 1.00 V. However, the experimental data for initial [E.sub.cell(ORP)] of 100 [cm.sup.2] unit cell V-RFB during the charging period was recorded at 1.263 V, which is higher than the estimated value. This is because the cycle of charge-discharge of V-RFB was delimited just before all the electrolytes species is completely consumed to prevent V-RFB operating under side reaction mode. This indicated that the experimental data does not represent the actual initial redox reactions of the species and the cell was not fully discharged during the previous charge-discharge cycle. This implies that the cell is operating within the safe mode of its SOC, which is above 20 % of depth of discharge.

Therefore, to match with the experimental data, the starting concentrations of V(III) and V(IV) were manually calculated and the results is as shown in Fig. 5.

Comparing the estimated data obtained from the calculation with the experimental data of 100 [cm.sup.2] unit cell V-RFB during the charging cycle, the concentration of V(III) and V(IV) in (9) should start at 0.82 mol [dm.sup.-3], a 2.4 % variance from the theoretical assumption of 0.80 mol [dm.sup.-3].

B. Effect of constant current efficiency

Fig. 6 illustrates the experimental [E.sub.cell(ORP)] compared to the estimated [E.sub.cell(ORP)] at different constant current efficiency in the range of [phi] = 0.5-1.0. The result shows the effect of applying different current efficiency in predicting [E.sub.cell(ORP)] during the charging cycle. In the simulation, current efficiency is kept constant throughout the charging process. For 100 % current efficiency ([phi] =1.0), the model matched the experimental cell potential at equilibrium but the predicted curve swings 5 % off the experimental curve in the middle of charging the V-RFB; this is the effect of the logarithmic function (Log10) in the Nernst equation. Note that the accuracy of the model decreases with decreasing current efficiency. For [phi] =0.5 and [phi] =0.7, the predicted model differs by 8 % and ~5 % from the experimental [E.sub.cell(ORP)], respectively.

Walsh [27] suggested that current efficiency in (3) should be varied during the duration of the reaction. Thus, the current efficiency in (8) is varied during the charging process of 1.6 mol [dm.sup.-3] V(III)/V(IV) in 4 mol [dm.sup.-3] [H.sub.2]S[O.sub.4] and the estimated result of [E.sub.cell(ORP)] is shown in Fig. 7. In the experiment, starting from 100 % current efficiency, it is reduced by 25 % for every 10 minutes of the reaction. The result shows that the error of the predicted [E.sub.cell(ORP)] is 2.3 % at the beginning of the reaction but the error reduces over time and on reaching equilibrium potential, it correctly predicts the [E.sup.o.sub.cell] of V-RFB.

C. Proposed potentiometric measurement of the 25 [cm.sup.2] unit cell V-RFB

Potentiometric measurement is a measure of kinetic reactions at working electrode compared to that at the reference electrode. Half-cell redox potentials and Open-circuit cell potentials are monitored using a divided, Open-circuit potentiometric cell via Hach Lange GmbH XR200 Hg/[Hg.sub.2]S[O.sub.4] reference electrodes (Part No. B20B200) and Sigma-Aldrich 6 mm, 99.9999 % graphite rod working electrode (Batch No. 11903BB) separated by an ion exchange membrane (DuPont Nafion NF115/[H.sup.+]).

With this method, varying the current efficiency is not required when estimating the [E.sub.cell(ORP)] as both half-cell potentials are measured against the standard Hg/[Hg.sub.2]S[O.sub.4] reference electrodes and the outcome of applying (9) is shown in Fig. 8.

Using this approach, the estimated [E.sub.cell(ORP)] of V-RFB system is more accurate compared to that obtained only from the working electrodes as the estimated curve fits the experimental [E.sub.cell(ORP)] of 25 [cm.sup.-2] V-RFB unit cell laboratory unit. Since OCV is a function of SOC, the same approach is extended to discharge cycle, and the estimated SOC of VRFB is as shown in Fig. 9.

VI. CONCLUSIONS

It should be noted that the use of Nernst equation and Faraday's law of electrolysis, with an appropriate manipulation of current efficiencies, *=0.1-1.0, able to predict the open-circuit potential of V-RFB, subsequently SOC of V-RFB. Two different approaches has been presented, direct estimation of [E.sub.cell(ORP)] compared to potential different between two working electrodes, which indicated by 2.3 % error. An improved estimated [E.sub.cell(ORP)] is observed with the proposed approach of a divided, Open-circuit potentiometric cell, via Hg/[Hg.sub.2]S[O.sub.4] reference electrodes and graphite rod working electrodes. The result shows the latter outperformed the former in estimating [E.sub.cell(ORP)],subsequently the SOC of the battery.

http://dx.doi.org/10.5755/j01.eee.19.3.1623

ACKNOWLEDGMENT

The authors are grateful to Re-Fuel Technology Ltd, Finchampstead, and Wokingham, UK for provision of equipment. Special appreciation to Prof. Walsh, Dr. Sharkh and P. Ridley for the discussions on V-RFB. All experiments were carried-out at the Electrochemical Engineering Laboratory, University of Southampton, UK.

REFERENCES

[1] I. Galkin, O. Teteryonok, and I. Milashevski, "Weight and size estimation of energy efficient LED ballasts", Elektronika ir Elektrotechnika (Electronics and Electrical Engineering), no. 4, pp. 55-60, 2012.

[2] P. S. Fedkiw, R. W. Watts, "A mathematical model for the iron/chromium redox battery", Journal of the Electrochemical Society, vol. 131, pp. 701-709, 1984. [Online]. Available: http://dx.doi.org/10.1149/1.2115676

[3] N. Tokuda, T. Kanno, T. Hara, T. Shigematsu, Y Tsutsui, A. Ikeuchi, T Itou, and T. Kumamoto., "Development of redox flow battery system", SEI Technical Review, pp. 88-94, 2000, no. 50.

[4] M. Skyllas-Kazacos, "Novel vanadium chloride/polyhalide redox flow battery", Journal of Power Sources, vol. 124, pp. 299-302, 2003. [Online]. Available: http://dx.doi.org/10.1016/S03787753(03)00621-9

[5] M. Skyllas-Kazacos, C. Menictas, "The vanadium redox battery for emergency back-up applications", in Proc. of the 19th International Telecommunications Energy Conference, INTELEC 97, 1997, pp. 463-471.

[6] A. Gonzalez, B. O. Gallachoir, E. McKeogh, K. Lynch, "Study of electricity storage technologies and their potential to address wind energy intermittency in Ireland", 2004. [Online]. Available: http://www.sei.ie/uploadedfiles/FundedProgrammes/REHC03001Fina lReport.pdf

[7] C. Menictas, D. R. Hong, Z. H. Yan, Y. J. Wilson, M. Kazacos, M. Skyllas-Kazacos, "Status of the vanadium redox battery development program", in National Conference Publication, Institution of Engineers, Australia, Sydney, USA, 1994, pp. 299-303.

[8] S. Eckroad, "Vanadium redox flow batteries: an in-depth analysis", Electric Power Research Institute, Palo Alto, CA 1014836, 2007.

[9] F. Mohammadi, P. Timbrell, S. Zhong, C. Padeste, M. Skyllas Kazacos, "Overcharge in the vanadium redox battery and changes in electrical resistivity and surface functionality of graphite-felt electrodes", Journal of Power Sources, vol. 52, pp. 61-68, 1994. [Online]. Available: http://dx.doi.org/10.1016/0378-7753(94)01938-X

[10] A. Tang, J. Bao, M. Skyllas-Kazacos, "Dynamic modelling of the effects of ion diffusion and side reactions on the capacity loss for vanadium redox flow battery", Journal of Power Sources, vol. 196, pp. 10737-10747, 2011. [Online]. Available: http://dx.doi.org/ 10.1016/j.jpowsour.2011.09.003

[11] A. A. Shah, H. Al-Fetlawi, F. C. Walsh, "Dynamic modelling of hydrogen evolution effects in the all-vanadium redox flow battery", Electrochimica Acta, vol. 55, pp. 1125-1139, 2010. [Online]. Available: http://dx.doi.org/10.1016/j.electacta.2009.10.022

[12] H. Al-Fetlawi, A. A. Shah, F. C. Walsh, "Modelling the effects of oxygen evolution in the all-vanadium redox flow battery", Electrochimica Acta, vol. 55, pp. 3192-3205, 2010. [Online]. Available: http://dx.doi.org/10.1016/j.electacta.2009.12.085

[13] M. R. Mohamed, S. M. Sharkh, H. Ahmad, M. N. Abu Seman, F. C. Walsh, "Design and development of unit cell and system for vanadium redox flow batteries (V-RFB)", International Journal of the Physical Sciences, vol. 7, pp. 1010-1024, 2012. [Online]. Available: http://dx.doi.org/10.5897/IJPS11.1555

[14] I. Snihir, W. Rey, E. Verbitskiy, A. Belfadhel-Ayeb, P. H. L. Notten, "Battery open-circuit voltage estimation by a method of statistical analysis", Journal of Power Sources, vol. 159, pp. 1484-1487, 2006. [Online]. Available: http://dx.doi.org/10.1016/j.jpowsour.2005.11.090

[15] S. Abu-Sharkh and D. Doerffel, "Rapid test and non-linear model characterisation of solid-state lithium-ion batteries", Journal of Power Sources, vol. 130, pp. 266-274, 2004. [Online]. Available: http://dx.doi.org/10.1016/j.jpowsour.2003.12.001

[16] F. C. Walsh, "Electrochemical cell reactions in metal finishing", Transactions of the Institute of Metal Finishing, vol. 69, pp. 111-116,

1991.

[17] S. Lee, J. Kim, J. Lee, B. H. Cho, "State-of-charge and capacity estimation of lithium-ion battery using a new open-circuit voltage versus state-of-charge", Journal of Power Sources, vol. 185, pp. 1367-1373, 2008. [Online]. Available: http://dx.doi.org/10.1016/j.jpowsour.2008.08.103

[18] T. Wu, M. Wang, Q. Xiao, X. Wang, "The SOC Estimation of Power Li-Ion Battery Based on ANFIS Model", Smart Grid and Renewable Energy, vol. 3, pp. 51-55, 2012. [Online]. Available: http://dx.doi.org/10.4236/sgre.2012.31007

[19] V. Pop, H. J. Bergveld, P. H. L. Notten, P. P. L. Regtien, "State-of-the-art of battery state-of-charge determination", Measurement Science and Technology, vol. 16, 2005.

[20] G. A. Ottewill, F. C. Walsh, "Electrode potential measurements", Transactions of the Institute of Metal Finishing, vol. 70, pp. 141-143, 1992.

[21] P. Trinidad, C. P. de Leon, F. C. Walsh, "The use of electrolyte redox potential to monitor the Ce(IV)/Ce(III) couple", Journal of Environmental Management, vol. 88, pp. 1417-1425, 2008. [Online]. Available: http://dx.doi.org/10.1016/j.jenvman.2007.07.007

[22] C. Blanc, "Modeling of a vanadium redox flow battery electricity storage system", Ph.D. dissertation, Laboratoire d'Electronique Industrielle Ecole Polytechnique Federale De Lausanne, Lausanne, 2009.

[23] C. Ponce-de-Leon, A. Frias-Ferrer, J. Gonzalez-Garcia, D. A.Szanto, F. C. Walsh, "Redox flow cells for energy conversion", Journal of Power Sources, vol. 160, pp. 716-732, 2006. [Online]. Available: http://dx.doi.org/10.1016/jjpowsour.2006.02.095

[24] P. Qian, H. Zhang, J. Chen, Y. Wen, Q. Luo, Z. Liu, D. You, B. Yi, "A novel electrode-bipolar plate assembly for vanadium redox flow battery applications", Journal of Power Sources, vol. 175, pp. 613- 620, 2008. [Online]. Available: http://dx.doi.org/10.1016/ j.jpowsour.2007.09.006

[25] C. Fabjan, J. Garche, B. Harrer, L. Jorissen, C. Kolbeck, F. Philippi, G. Tomazic, F. Wagner, "The vanadium redox-battery: an efficient storage unit for photovoltaic systems", Electrochimica Acta, vol. 47, pp. 825-831, 2001. [Online]. Available: http://dx.doi.org/ 10.1016/S0013-4686(01)00763-0

[26] F. Rahman, I. O. Habiballah, M. Skyllas-Kazacos, "Electrochemical behavior of vanadium electrolyte for vanadium redox battery-a new technology for large scale energy storage systems", in Proc. of the Cigre, 2004, pp. 1-8.

[27] F. C. Walsh, A first course in electrochemical engineering. Romsey: The Electrochemical Consultancy (Romsey) Ltd., 1993.

M. R. Mohamed (1), H. Ahmad (1), M. N. Abu Seman (2)

(1) Sustainable Energy & Power Electronics Research (SuPER) Group, Faculty of Electrical & Electronics Engineering, Universiti Malaysia Pahang, 26600 Pekan, Pahang, Malaysia

(2) Faculty of Chemical Engineering & Natural Resources, Universiti Malaysia Pahang, Lebuhraya Tun Razak, 26300 Kuantan, Pahang, Malaysia rusllim @ ump.edu.my

Manuscript received April 27, 2012; accepted November 18, 2012.

This work was supported by The Malaysian Ministry of Higher Education (MOHE) and Universiti Malaysia Pahang (UMP). On-going experiment is supported by UMP under grant RDU120346.


TABLE 1. NOMENCLATURE

[C.sub.V(II)],           Concentration     V(II),     Vanadium
[C.sub.V(III)],           of vanadium      V(III)    species at
[C.sub.V(IV)],            species at       V(IV),     different
[C.sub.V(V),]              different        V(V)      level of
                           level of                   oxidation
                           oxidation                    state
                          state, mol
                          [dm.sup.-3]

[C.sub.oxd]              Concentration       F         Faraday
                          of oxidised                constant, F
                         species, mol                 = 96485 C
                          [dm.sup.-3]                [mol.sup.-
                                                         1]
[C.sub.red]              Concentration       I        Constant
                          of reduced                  current/A
                         species, mol
                          [dm.sup.-3]
[E.sub.cell]                 cell            R        Molar gas
                          potential,                  constant,
                           measured                    8.3145
                          across unit                [JK.sup.-1]
                          cell stack                 [mol.sup.-
                                                         1]
[E.sub.cell(ORP)]            open-           z        Number of
                         circuit cell                 electrons
                           potential                 transferred
                          across two                 in the cell
                          electrodes,                 reaction
                           otherwise
                          abbreviated        T      Temperature/K
                              as
                       [E.sub.cell(ORP)]
                              for
                          oxidation-
                           reduction
                           potential
[E.sup.o.sub.cell]       Standard cell       t         Time/s
                           potential
[E.sup.o]                  Standard          V        Volume of
                           electrode                electrolyte/
                           potential                 [dm.sup.3]
[E.sub.v(III)/V(II)]       Positive                    Current
                           half-cell                 efficiency
                           potential
                           for V-RFB
[E.sub.V(IV)/V(V)]         Negative         SHE       Standard
                           half-cell                  hydrogen
                           potential                  electrode
                           for V-RFB
COPYRIGHT 2013 Kaunas University of Technology, Faculty of Telecommunications and Electronics
No portion of this article can be reproduced without the express written permission from the copyright holder.
Copyright 2013 Gale, Cengage Learning. All rights reserved.

Article Details
Printer friendly Cite/link Email Feedback
Author:Mohamed, M.R.; Ahmad, H.; Abu Seman, M.N.
Publication:Elektronika ir Elektrotechnika
Article Type:Report
Geographic Code:9MALA
Date:Mar 1, 2013
Words:3969
Previous Article:Methods of improving superconductive fault current limiting devices in power engineering.
Next Article:Analysis of heat sink modelling performance.
Topics:

Terms of use | Privacy policy | Copyright © 2020 Farlex, Inc. | Feedback | For webmasters