**3. Results and Discussion**

#### *3.1. Battery Performance for the Baseline Case*

As a baseline case, the VRFB stack was operated at power scale factor (SP) of 1/2 and time scale factor (ST) of 1/2 with electrolyte volume of 30 L in each tank. The 7-day battery profile shown in Figure 2b was discretized into constant power time steps of 5.5 min and was imposed on the stack using the battery cycler. OCV was measured after every time step over a period of 1 min during which the battery power was set to zero. The battery cycler was programmed in such a way that if the intended power during a particular time step could not be delivered to or drawn from the battery, then that power step would be aborted, and the testing would continue to the next step which would be the OCV measuring step. At the end of the OCV step, the next power step would be imposed. Thus, battery failure would be indicated by a power step that did not last the full duration of 5.5 min. During the whole experiment, the voltage and current across the battery were measured at 5 s intervals. Prior to each run, the battery was charged until the stack voltage reached the pre-set value of 1.7 V per cell.

The response of the battery to the imposed power steps is depicted in Figure 3a which shows the variation of power and SoC over the seven-day period. (It may be noted that the total duration of each experiment would depend on the time scale factor as well as on the number of failures and the number of OCV steps and would therefore change from run to run. For ST of 1/2, if the OCV measurement steps are discounted and if there are no charging or discharging failures, then the duration would be 84 h). The experiment started at midnight of the first day, and thus, with a discharge step and would then go continuously over a series of charging and discharging steps and would finish with a partial discharge of the 7th day. The SoC obtained using measured OCV is also plotted in the figure. One can see that the power variation follows the expected variation and that the steep changes in power are easily handled by the battery. The repeated variation of SoC over a wide range without lasting ill effects on the battery is also noteworthy. The full range of SoC of the battery is thus being utilized and this is an important feature of the vanadium flow battery.

One can also see in Figure 3a several instances of failure of the stack to deliver or absorb the required amount of power. Charging failures occur when the SoC is very high and discharging failures occur at very low SoC values. An expanded view of one such discharging failure is shown in Figure 3b which shows repeated failure to execute discharge power step over the simulation period of 13.6 h to 14.3 h. During this period, the SoC is particularly low (~9%) and the stack was unable to discharge even 120 W of power. (More power could have been extracted from the battery by increasing the electrolyte circulation rate or decreasing the power; however, such active management of the electrolyte was not done in the present study). An instance of battery failure during charging is shown in close-up view in Figure 3c which shows charging failure towards the end of charging on the 7th day over the period 74.3 to 75 h. One can see that the SoC is rather high at around 92%. Figure 3d shows the nomenclature used in the present study to characterize battery failure to deliver by time and energy. Typically, the stack will be able to meet the power demand for part of a power step and it may then fail for the rest of the duration of the time step. Cumulative amounts of time during which the power demand has not been met is used to determine battery failure by time. The shaded areas in Figure 3d represent the amount energy demand that has not been met. This is used to determine the cumulative battery failure % by energy.

**Figure 3.** *Cont*.

**Figure 3.** VRFB performance for SP = 1/2 and ST = 1/2 showing with 30 L electrolyte: (**a**) Complete 7-day profile with SoC variation. (**b**) Discharge failure in 1st discharge cycle. (**c**) Charge failure in 7th day charge. (**d**) Schematic diagram of battery with failure to deliver power and without failure.

The daily changes in energy flows during charge and discharge are listed in Table 2. One can see the amount of energy output from the battery during the 1st charge is only 419 Wh and the profile requires the battery to discharge up to 1100 Wh on certain days. Due to depletion of stored energy, its SOC becomes so low that it has been unable to deliver the load demand requirement. The battery is able to accommodate the charge energy from PV during the 2nd day of insolation but is not able to deliver again during the early morning of the 2nd night discharge as the intended discharge energy is 10% higher than what the battery has been able to absorb during the 2nd charge while the amount of energy put in during the 2nd day charging is only 10% higher than what battery is expected to discharge in the night. Third day's charging is of high energy content and the battery fails briefly towards the end of the charging time because the SoC has reached 95% and it is unable to accommodate the amount of energy coming in at the high power of 570 W. The high energy input during the third day means no discharge failures on the 3rd night. The relatively lower amounts of charge on the 4th and the 5th day of charging lead to discharge failures on the succeeding discharging events. The amount of energy charged on the 6th day is the highest among the seven-day profile; as a result, the battery gets fully charged resulting in

no discharge failure on the 6th day. The last day's charge too is considerable and due to the high SoC at the beginning of charge (~25%), the battery soon gets fully charged leading to extensive charging failure on the last day and no discharge failure during the last night.

Table 3 shows the details of energy delivered and charged for various charge and discharge cycles. Energy-based % failure and time-based % failure for each case is also tabulated. Minor (1–2%) energy-based failures without corresponding time-based failures can be neglected as errors due to fluctuations in battery power supplied by the battery cycler. One can see that significant discharge failure has occurred in 1st, 2nd, 4th, and 5th discharges and significant charge failures in the 3rd, 6th, and 7th charges. The first discharge failure may be attributed to the exceptionally low insolation on the first day from an already depleted battery and is thus caused by initial conditions of the set-up. (In view of this, subsequent runs have been done with second day's half discharge.) The 3rd and the 4th discharge failures may be attributed to the large amount of discharge that needed to be done. The more severe 5th discharge failure is somewhat surprising as the amount of discharge energy is smaller and the amount of charge energy in the preceding charge is higher. However, as can be seen in Figure 3a, the SoC at the beginning of discharge is lower than that at the corresponding stage of the 3rd and 4th discharges. Thus, discharge failures are associated with low SoC rather than high power under typical residential load conditions. In contrast, charge failures are a combination of high power and high SoC (compare the conditions of the 3rd, 6th, and 7th day charge failures in Figure 3a) as the charging power is significantly higher than the average discharging power in solar PV-residential load integration applications.


**Table 3.** VRFB energy during charge/discharge cycle 30 L for SP = 1/2, ST = 1/2.

#### *3.2. Power and Energy Scaling Studies*

In order to study the influence of electrolyte volume, and hence the battery system's energy storage capacity, on the dynamic performance of the integrated system, experiments have been carried out with the electrolyte volume increased from 30 liters to 35 liters on each side and then once again from 35 liters to 40 liters. The same stack operated with the same voltage limits and electrolyte circulation rates was used in these simulations. Thus, compared to the baseline case, the power scaling remains the same but energy storage capacity has been increased by 16.6% and 33%, respectively. As mentioned earlier, the

ordering of the days has been changed from 1-2-3-4-5-6-7 to 2-3-4-5-6-7-1 to remove the anomalous influence of the starting day. The battery response in terms of power and SoC in these two cases is compared in Figure 4. It can be seen the first day discharging failures have disappeared but mid-week discharge failures are still there, though with reduced intensity, especially in the case with 40 L electrolyte volume on each side. In both cases, the mid-week discharge failures are associated with the battery reaching very low SoC despite increased storage capacity compared with the baseline case. Thus, increasing the electrolyte volume is beneficial in reducing discharge failures. Charge failures too have come down significantly, especially in the 40 L case in which instances of high SoC have reduced considerably.

**Figure 4.** Battery performance with SoC variation for SP = 1/2 and ST = 1/2 for (**a**) 35 L electrolyte (**b**) 40 L electrolyte and (**c**) with 40 L electrolyte with SOC variation for SP = 1/2 and ST = 1/3.

In the above two cases, the total energy intended to be traded is the same as that in the baseline case; only the energy storage capacity of the battery system is increased

by increasing the electrolyte volume. Figure 4c shows the response for a stack with 40 L of electrolyte which is run on the same power scaling of SP = 1/2 but with a time scaling of ST = 1/3. This system has the same energy storage capacity as that of Figure 4b but the energy traded is reduced by 1/3rd. Thus, this experiment is equivalent to SP = 1/2 with ST = 1/2 scaling with 60 L of electrolyte at initial SoC of around 60% for the same battery stack. As can be seen from Figure 4c, there are no discharge failures as the SoC remains comfortably high (>40%) throughout the equivalent seven-day cycle. However, the battery has more charging failures because the SoC reaches high values (>90%) repeatedly. However, this failure to charge does not translate to failure to meet load demand because the system has high storage capacity (twice as much as that of the reference case).

Figure 5 compares the energy traded (charged or discharged) in every charge/discharge cycle over the seven days for the three cases shown in Figure 4. In addition, given here is the intended amount of energy to be traded in each cycle. All the three cases (of 35 L with SP = 1/2 and ST = 1/2, 40 L SP = 1/2 and ST = 1/2 and 40 L with SP = 1/2 and ST = 1/3) have been non-dimensionalized by dividing the energy by the maximum energy traded in that seven-day period (this corresponds to the charging energy on the 6th day). It can be seen that the combination of (40 L, SP = 1/2 and ST = 1/3) is able to deliver discharge energy as intended over the entire period; however, there is considerable wastage of PV output. This is borne out by the SoC variation which is mostly in the range of 60 to 99% showing underutilization of the electrolyte. The intermediate case of (40 L, SP = 1/2 and ST = 1/2) is better at utilizing the PV output with occasional discharge failure while the case with (35 L, SP = 1/2 and ST = 1/2) may be said to be undersized with respect to energy storage capacity. Proper energy sizing of the energy system is necessary to optimally use its storage capacity.

**Figure 5.** Comparative plot showing traded energy (%) in each charge/discharge cycle over a seven-day period for a VRFB with (electrolyte volume, SP and ST) combinations of (35 L, 1/2, 1/2), (40 L, 1/2, 1/2) and (40 L, 1/2, 1/3).

In order to bring out the effect of stack sizing, a further simulation has been carried with an electrolyte volume of 40 L but with SP = 1. In view of the limited energy storage capacity associated with 40 L electrolyte volume, the time scale factor is reduced such that ST = 1/5 leading to SE of 1/5 compared to that of 1/4 for the baseline case. The reduced energy scaling is consistent with anticipated higher efficiency losses associated with higher powers of charge and discharge due to doubling of power compared to the baseline case.

The response of the battery system for the first two days is summarized in Figure 6. One can see that high power charging leads to significantly higher overpotential so that charging failure occurs on the first day itself even for SoC < 80% and the SoC remains less than 90% at the end of first day's charging. As a result, there is a hint of failure at the far end of the first full discharge. Due to high charging losses, the SoC does not even reach 80% at the end of 2nd day's charging. This is in contrast to the corresponding case in Figure 4b where the SoC is well in excess of 90% at the corresponding stage. Coupled with this low SoC, higher discharge losses due to higher average discharge power leads to extensive failure in the next discharge cycle (not shown) which has a knock-on effect on subsequent charge and discharge cycles, each of which suffers from extended periods of battery failure to meet power demand. This case, which is representative of an undersized stack, thus illustrates the importance of power sizing of the integrated system. The battery should be able to tackle high charging powers; otherwise, subsequent discharge and charge cycles will suffer.

**Figure 6.** Battery performance with 40 L electrolyte with SoC variation for SP = 1 and ST = 1/5.

#### *3.3. Charging and Discharging Efficiency*

From measured OCV at the end of every power step, the average overpotential for every step could be determined. From this, the charging efficiency and discharging efficiency could be computed over the entire seven-day period for a given integrated system. For a given VRFB stack operating at a constant electrolyte circulation rate, both efficiencies depend primarily on the power at which charge or discharging takes places and the SoC of the electrolyte, both of which vary dynamically in a given situation. Figure 7 shows the data of charging and discharging efficiencies over the seven-day period wherein data from for all the three cases shown in Figure 4 are plotted together. One can see that the discharge efficiency is not strongly influenced by power (probably because the discharging power is low and varies in a rather narrow range) and remains relatively high (~0.95) for SoC > 30%. On the contrary, the charging efficiency is a strong function of power and almost varies linearly with charging power. Since charging power is about three times higher than the discharging power, the average charging efficiency is lower at about 0.9.

**Figure 7.** Efficiency variation with SoC and operating power of VRFB for (**a**) discharging and (**b**) charging for the three runs shown in Figure 4.

#### *3.4. Lead Acid Battery Performance*

The same 7-day profile is operated using a lead-acid battery for understanding its performance to dynamically changing requirements. A new lead-acid battery of 150 Ah capacity at 12 V was used for these experiments. Since the commercial lead acid battery has

a power rating of 180 W and energy rating of 1800 Wh, a power scaling factor, SP, of 1/8 and a time scale factor, SF, of 1 were used giving energy scaling factor, SE, of 1/8. Since ST = 1, each power step lasted 11 min; this was followed by a one-minute OCV measurement step. Figure 8 shows the battery response for the seven-day profile in terms of power step by power step response (Figure 8a) and in terms of normalized cumulative energy traded in each charge/discharge step (Figure 8b) where the data for the VRFB case of 40 L electrolyte volume, SP = 1/2 and ST = 1/2 are also given. One can see from Figure 8a that the lead-acid battery suffers charging failures on each of the first six days; however, due to its high energy storage capacity (and favorable power scaling), it shows no failures in discharge. Figure 8b shows that in comparison with VRFB, the energy charged in each cycle is significantly less in charging cycle. On the other hand, it outperforms the VRFB in discharge as it is able to meet the discharge demand in every cycle. However, it must be kept in mind that the lead acid battery case has an energy scaling factor of 1/8 whereas SE for the VRFB is 1/4. Given that the rated energy storage capacity of the former is 1800 Wh compared to about 1000 Wh for the latter, the lead acid battery system is grossly underutilizing its energy storage capacity.

**Figure 8.** (**a**) Lead acid battery performance for SP = 1/8 and ST = 1. (**b**) Energy comparison for VRFB with 40 L with SP = 1/2 and ST = 1/2 with 2 lead acid battery performance.

It may further be noted that the VRFB system worked well for about 50 consecutive charge + discharge cycles without noticeable degradation in performance whereas the new lead acid battery showed signs of rapid degradation. After three seven-day profile experiments were conducted with SP of 1/8, 1/6 and 1/4, the battery was found to have retained a capacity of only 50 Ah. When the seven-day profile was repeated with SP of 1/8, the reduced capacity was found to have led to extensive failures in both charging and discharging. Although this cannot be considered as a well-controlled study of degradation behavior of the lead acid battery (which was procured off-the-shelf from a commercial store), the VRFB system does have the advantage of long life under repeated cycles which is necessary for solar PV applications.
