Experimental study on the energy loss from flow and electrical of vanadium battery with constant pump frequency

When the vanadium battery was running, pump frequency and current density were two frequently adjusted parameters. When the pump frequency was constant, the main flow-electrical parameter variation needs to be further studied. To this end, a 10 kW vanadium battery was built. When the current density was relatively high during the charge-discharge, the flow-electrical parameters of the cathode and anode including the temperature, flow resistance, turning voltage difference, capacity loss, energy loss and energy efficiency were studied. Besides, the compositions of capacity and energy were introduced, and the loss calculation scheme was proposed. Firstly, in flow analysis, the flow resistance was defined, which represents the flow state of the electrolyte. It was found that the flow resistance was nearly linear with the temperature. Secondly, in electric analysis, the turning voltage difference increased with the current density increasing. For the same current density, the total energy loss of charge was less than the discharge, and the energy loss of bypass was less than the internal resistance. With the current density increasing, the energy efficiency decreased. The research can be provided insight into the optimizing operation for the vanadium battery.


Introduction
The vanadium redox flow battery (VRFB) has a good prospect in large-scale energy storage.The structure of the vanadium battery was shown in Figure 1.The catholyte ( + 3 V / + 2 V ) and anolyte ( + 4 V / + 5 V ) were respectively stored in two tanks, and the electrolyte was circulated between the stack and the tank through the pump.The catholyte and anolyte were separated from each other in the stack cell by the diaphragm that only allows protons to pass through.When the power or load was applied to the VRFB through the AC/DC converter, a chemical reaction occurs on the electrode to change the valence of vanadium ion, and the electric energy will be stored or released through the collector [1].The flow rate and current density were the main parameters to be considered for the long-term operation of the VRFB.On the one hand, the general rules that the VRFB performance was affected by flow rate or current density were analyzed by scholars.In 2017, the impact of flow rate change was predicted based on numerical simulation [2].The coulomb efficiency and battery performance can be improved when the electrolyte flow rate was higher and the charge time was longer.For the threedimensional small size single battery, a quasi-static thermal analysis model was used to simulate the influence of current density and flow rate on the thermal [3].It was pointed out that heat generation strongly depends on the current density.As the current density increases, the heat from the chemical reaction increased proportionally.The temperature distribution was more uniform due to the faster flow.On the other hand, the flow rate or current density was optimized by scholars to improve the VRFB performance.The electrolyte flow rate output feedback control scheme was proposed for the VRFB of 5 kW/15 kWh with 40 cells [4].The proportional integral controller was used for reaching the same performance with the lower flow, and the pump loss was only 31% of that before the improvement.Moreover, the appropriate flow rate (0.0022~0.0052 /s m 3 ) of the 40 kW vanadium battery system was proposed [5].Three coefficients of the flow model were determined and adjusted according to the operating parameters.The system efficiency increased by 3.34% by controlling the electrolyte flow.
The general influences of flow rate and current density on the VRFB performance were done by scholars.However, for the VRFB of larger power with multiple cells, when the pump frequency was unchanged, more details of flow and electrical characteristics needed to be further studied, and so as to provide better support for operating parameters optimization in the future.

Experiment design and analysis scheme
For the VRFB system, the experimental stack was 10 kW, with 38 cells connected in series.The flow channel thickness was 3 mm, the bipolar plate thickness was 1 mm, and the proton exchange membrane thickness was 25 μm.The effective area of carbon felt was 1100 2 cm and the compression ratio was 17%.The concentration of vanadium ion and sulfuric acid were 1.6 mol/L and 4.2 mol/L respectively.The volume of the electrolyte tank was 500 L. The electrolyte volume of cathode and anode were both 350 L. The PVC pipe was used for all pipelines.The effective lift of the magnetic pump was 18 m, and the maximum power was 2.2 kW.The SIEMENS PLC was used for the control system.
The experimental conditions were as follows.The stack structure of VRFB was fixed, and the chargedischarge cycle test was conducted with a constant current.The pump frequency was 55 Hz.The current densities were 120, 150 and 180 mA/ 2  cm respectively.The cut-off voltage for cell charge-discharge was 1.1 V-1.65 V. When the cut-off voltage was reached, the charge or discharge was stopped, the electrolyte circulating was maintained, and then the charge or discharge mode was switched.The pressure sensor, thermodetector and flowmeter were installed at the inlet and outlet of the stack to detect the pressure, temperature and flow respectively.The Newwell charge-discharge device was used to carry out the test.The stack voltage was detected with the control system.
For the three categories including cathode and anode, charge and discharge, and same and different current densities, the analyses of flow and electric parameters were carried out.Firstly, in flow analysis, temperature, pressure difference and flow rate were the important parameters.The temperature and flow resistance that varied with current density were discussed in detail.Moreover, the relationship between temperature and flow resistance was analyzed.Secondly, in electric analysis, current, voltage, capacity, capacity loss, energy, energy loss and battery efficiency were the key parameters.The current and the voltage waveform features at the initial stage of charge-discharge were analyzed.Besides, the compositions of the current and the voltage were introduced.The capacity and energy were deduced from the current and the voltage.In particular, the loss classification was proposed including the flow channel and the transfer for the capacity, and including the internal resistance and the bypass for the energy.Also, the characteristics of capacity loss and energy loss were analyzed.Lastly, cell efficiencies were discussed.

Characteristics of temperature and flow resistance
The differential pressure and flow rate were two key parameters for battery operation.The electrolyte circulation was maintained by differential pressure.The electrochemical reaction rate was affected by the flow rate.The pressure difference was mainly caused by the carbon felt and the flow channel.The electrolyte flow was hindered by the porous structure of the felt, the resistance of the pipe wall and the sudden change of the flow channel shape, causing the pressure loss.Here, to unify pressure difference and flow rate, flow resistance (Pa.min /L) was defined as the ratio of pressure difference (Pa) to flow rate (L/min), representing the flow state of the electrolyte.
In the formula, The temperature and flow resistance of different current densities at the cathode and anode during charge -discharge were shown in Figure 2. The average temperature and the average flow resistance were used during multiple charge-discharge cycles at a certain current density, and the charge and discharge were represented by the C and the D respectively.For the same current density, the temperature in descending order was cathode discharge, anode discharge, cathode charge and anode charge.It can be concluded that the temperature of cathode was higher than that of anode, and the discharge was higher than that of charge.Also, for the same current density, the flow resistance from large to small was anode charge, anode discharge, cathode charge and cathode discharge respectively.It can be seen that the flow resistance of cathode was smaller than that of anode, and the discharge was smaller than that of charge.As the current density increased, the temperature increased, and the flow resistance decreased accordingly.The trends of the temperature were opposite to the flow resistance.When the current density varies from 120 to 180 2 mA/cm , the maximum temperature difference was 1.52 ℃ in the case of cathode charge.The maximum flow resistance difference was 0.10 Pa .min /L in the case of cathode charge.The polynomial fitting was used to analyze the relationship between the temperature and flow resistance, as shown in Figure 3.It can be briefly analyzed as follows.There was a quasi-linear relationship between temperature and flow resistance.At the same temperature (more than 33 ℃), the charge flow resistance was less than the discharge, and the cathode flow resistance was less than the anode.When the temperature rises, the difference in flow resistance increased for the charge and discharge, as well as for the cathode and anode.For the temperature from 35 ℃ to 40 ℃, the maximum flow resistance difference was 0.38 Pa .min/L in the case of cathode charge, and the minimum flow resistance difference was 0.30 Pa .min/L in the case of anode discharge.

Waveform characteristics of current and voltage
The current used in charge-discharge was represented by the step function, as shown in Figure 4  The turning point of the voltage waveform and the corresponding voltage difference at the initial stage of charge-discharge were shown in Figure 4(c) and Figure 4(d) respectively.Here, the slope change was used to trace the turning point.It was concluded that the slope was changed obviously at the turning point.The turning voltage difference(TVD) was defined as the voltage difference between the charge-discharge beginning and the waveform turning at the initial stage of charge-discharge.The cell resistance could be reflected by the TVD.For the same current density, the TVD of discharge was smaller than that of the charge.When the current density increased, TVD increased.When the current densities rose from 120 to 180 2 mA/cm , the TVDs increased by 0.75 V and 1.05 V for charge and discharge respectively, as shown in Figure 4(d).

Characteristics of capacity loss and energy loss
In charge-discharge, the current loss was produced due to the flow channel and diaphragm.The voltage loss resulted from the combination of charge-discharge current and cell internal resistance.The capacity loss and energy loss were caused by the loss of current and voltage.
The charge-discharge current was divided into two parts including ideal current and total leakage current.The total leakage current was also divided into two parts including flow channel leakage current and transfer leakage current, as shown in follows.

( ) ( ) ( ) ( )
where ( ) ( ) and ( ) were respectively the charge-discharge current, ideal current, flow channel leakage current and transfer leakage current.( ) R was the flow channel resistance, and c i was the pipeline system leakage current.ρ , L and S were the electrolyte resistivity, flow channel length and flow channel cross-sectional area respectively.1 k was the membrane conductivity coefficient, and 2 k was the current change due to ions through the membrane.The capacity was the time integral of the current.Corresponding to the current, the capacity was calculated as follows.
( ) ( )dt where ( ) ( ) ( ) ( ) The capacity and loss of charge-discharge were shown in Figure 5.The cumulative value of capacity was used in Figure 5(a) and Figure 5(c).The average value of capacity during charge-discharge was used in Figure 5(b) and Figure 5(d).In Figure 5(c) and Figure 5(d), the total loss, the flow channel loss and the transfer loss of capacity were represented by the CTL, CFL and CRL respectively and the 120, the 150 and the 180 were the values of current density.As shown in Figure 5(a), for the same current density, the capacity increased during charge, and decreased during discharge.As the number of cycles increased, the capacity at the end of discharge increased continuously.As shown in Figure 5(b), when the current density increased, the charge capacity and discharge capacity decreased, and the charge capacity was less than the discharge.As shown in Figure 5(c), for the same current density, as the number of cycles increased, the capacity loss increased continuously, and the transfer loss was greater than the flow channel loss.As shown in Figure 5(d), with the increase of current density, the total capacity loss decreased.For the capacity loss of the total, transfer and flow channel, the charge was less than the discharge.
The calculation methods for the loss of voltage energy.The charge-discharge voltage was the sum of voltage loss and ideal voltage from the Nernst equation, as shown in follows.
( ) ( ) ( ) where ( ) were respectively charge-discharge voltage, ideal voltage and voltage loss.SOC , + H c and n were state of charge, proton concentration, and number of cells respectively.i R was the cell internal resistance.The energy was the time integral for the product of voltage and current.Here, energy loss was divided into two parts including internal resistance loss and bypass loss, which was calculated as follows.
( ) ( ) ( )dt where ( ) ( ) ( ) ( ) were respectively the total energy, ideal energy, bypass energy loss and internal resistance energy loss.The energy and energy loss were shown in Figure 6.The cumulative value of energy was used in Figure 6(a) and Figure 6(c).The average values of energy during charge and discharge were used in Figure 6(b) and Figure 6(d).In Figure 6(c) and Figure 6(d), the total loss, the internal resistance loss and the bypass loss of energy were represented by the ETL, EIL and EBL respectively.As shown in Figure 6(a), for the same current density, the charge energy increased, and the discharge energy decreased.As the number of cycles increased, the energy at the end of discharge increased continuously.As shown in Figure 6(b), with the increase of current density, the charge energy and the discharge energy decreased, and the charge energy was less than the discharge energy.As shown in Figure 6(c), for the same current density, with the increase of the number of cycles, the energy loss of charge or discharge increased continuously, and the energy loss of bypass was less than that of internal resistance.As shown in Figure 6(d), with the same current density, the energy loss of charge was less than that of discharge, and the internal resistance energy loss was over 70% of the total energy loss.The battery efficiency of the charge-discharge was shown in Figure 7.The results show that with the increase of current density, the coulomb efficiency(CE) increased, while the voltage efficiency(VE) and energy efficiency(EE) decreased.As the current density increased from 120 to 180 2 mA/cm , the CE increased by 1.54%, and the VE and the EE decreased by 3.94% and 2.43% respectively.The coulomb efficiency has the smallest variation.

Conclusions
The flow and electric characteristics were summarized in the following three aspects.Firstly, the flow parameters were discussed.When the current density increased, the temperature continued to rise, and the flow resistance continued to decrease at the cathode and anode.The temperature was approximately linear with the flow resistance.Secondly, the electrical parameters were analyzed.For the same current density, the TVD of discharge was smaller than that of the charge.As the current density increased, the TVD increased at the initial stage of charge-discharge.The calculation scheme of capacity loss and energy loss derived from the current and voltage was proposed.In particular, the loss classification was also proposed.For the same current density, with the increase of the number of cycles, the energy loss during charge-discharge increased continuously, and the loss of bypass was less than that of internal resistance.For the same current density, the total energy loss of charge was less than discharge, and the loss of bypass was less than that of internal resistance.Lastly, with the increase of current density, the coulomb efficiency increased, while the voltage efficiency and the energy efficiency decreased.When the pump frequency was fixed, studying the loss variation of flow-electric parameters can be helpful to improve the operation efficiency of the VRFB.

Figure 1 .
Figure 1.Structure of the all vanadium redox flow battery drop caused by carbon felt, flow channel and structure mutation respectively, and r F , p Δ and Q were the flow resistance, pressure drop and flow rate respectively.felt p Δ was affected by thickness, permeability, cross-sectional area of electrode, and flow rate and viscosity of electrolyte.channel p Δ was affected by the length, the diameter, the cross-sectional area of the flow path, and flow rate and viscosity of electrolyte.structure p Δ was affected by the shape and size of the flow channel.

Figure 2 .
Temperature and flow resistance change with current density in the charge-discharge: (a) Temperature; (b) Flow resistance.

Figure 3 .
Figure 3. Relation between temperature and flow resistance.
(a).The voltage waveform was shown in Figure 4(b).For the different current densities, the charge time and discharge time decreased with the current density increasing.When the current density rose from 120 to 180 2 mA/cm , the charge time and discharge time dropped 3640 s and 3395 s respectively for the first four cycles, as shown in Figure 4(b).

Figure 5 .
respectively total capacity, ideal capacity, flow channel capacity loss and transfer capacity loss.Capacity and loss of charge-discharge: (a) Capacity with time; (b) Capacity with different current densities; (c) Capacity loss of total, flow channel and transfer with time; (d) Capacity loss of flow channel and transfer with different current densities.
Energy and loss of charge-discharge: (a) Energy with time; (b) Energy with different current densities; (c) Energy loss of total, bypass and internal resistance with time; (d) Energy loss of bypass and internal resistance with different current densities.

Figure 7 .
Figure 7. Battery efficiency varying with current density.