*2.5. Estimation of State of Charge (SoC) of the Battery*

State of charge (SoC) of the battery, which represents the fractional energy remaining in the battery for discharge, is an important parameter in assessing battery integration with upstream and downstream equipment. In the present study, SoC has been estimated from measurements of the open circuit voltage (OCV) of the stack at frequent intervals during each run. A single cell using the same materials and methods used to construct the stack was assembled and charge-discharge cycling was done at constant current densities for a single VRFB cell with 1 liter of vanadium electrolyte each as positive and negative electrolyte. OCV of the cell was measured with specified amount of change in SoC intermittently during charge and discharge. At moderate current densities, the overpotential during charge and discharge at a particular SoC value was found to be nearly the same in the SoC range of 20 to 80%. An average of the two curves is taken to be OCV and these

data have been used to obtain a correlation between SoC and OCV which then has been used to estimate the SoC dynamically using measured value of the OCV.

#### *2.6. Set-Up of the Experimental Study*

A comparison of the load and supply profiles over a seven-day period is shown in Figure 2a. Figure 2b shows the difference between the two; this is the power that would be drawn from or sent to the battery. As remarked earlier, the residential load is fairly constant compared to the large spikes in solar output. There is also considerable variation in the day-to-day energy output from the PV. The integrated PV-battery-load system should be able to work with these typical variations and still deliver as much power as demanded by the consumer at every moment. For the integrated system to perform effectively, the individual systems should be properly scaled so that the systems are not too oversized nor too undersized. The performance of the integrated system—in terms of being able to meet the load demand at any instant, being able to use PV output for either meeting the load or charging the battery and for the battery to operate at high charging /discharging efficiencies—and its relation to the sizing of the components is of interest to the present study.

Examination of the load and supply profiles shows that on the whole, there is considerable overlap between the two. In energy terms, this PV self-consumption (PVSC) amounts to about 23.4% of PV output that can go directly to the load during the sunshine hours; the rest of the 76.6% of load needs to be met through battery which is charged by the PV, assuming the system to be working independently of the grid. Keeping these numbers in view, the sizing of the PV and the battery is done as follows. Over the seven-day period in consideration, the residential load amounts to 39.9 kWh. Assuming the PV to be oversized by a factor of 25% (given the rather wide variations in the day-to-day energy output from the PV), the PV system is nominally rated at 50 kWh. The energy output per day is scaled as per Figure 2a which reflects measured day-to-day variation over a week in June 2019. The battery power profile is simulated as the difference between the power from PV and load demand and is shown in Figure 2b. This data (see also Table 2), with a scale factor, constitutes the input to Bitrode battery cycler to simulate the dynamic changes in PV-battery-load integrated system.

**Table 2.** Daily energy variations for PV, load and battery in Wh with an energy scaling factor, SE, of 1/4 (C-charge, DC-discharge).


The experiments were designed to operate the battery with scaled down factors and varying electrolyte volumes to understand the stack performance for varying energy and power demand. Keeping in mind different power and energy characteristics of the two battery systems used in the present study, a power scale factor, SP, an energy scale factor, SE, and a time scale factor, ST, have been varied independently while maintaining the relation that SE = SP × ST. Thus, having SP = 1/2, SE = 1/2 and ST = 1 will simulate an integrated system with a total weekly solar energy input of 50/2 = 25 kWh. If ST is changed to 1/2 while keeping SP to be 1/2, the energy input to the system will be reduced to 12.5 kWh over the week. Given that the VRFB system has a high power to energy ratio, for VRFB studies, experiments were conducted with SP of 1 (full scale) or 1/2, ST of 1/2 or 1/3 or 1/5 resulting in SE of 1/4 or 1/5 or 1/6. The lead-acid battery has a rated P/E of 1/10. Therefore, it has been operated at SP of 1/6 and 1/8 with ST of 1 giving an SE of 1/6 or 1/8. It may be noted that these scale factors refer only to traded energy; the inherent maximum energy storage capacity or power delivery capacity depend on the state of the battery and the operating conditions, including the volume of electrolyte and stack size and cell characteristics in the case of VRFB and nominal factory rating in case of the lead-acid battery.

In the experiments, the actual power vs. time profiles of the battery (shown typically as in Figure 2b) are imposed on the battery through a battery cycler such that the predetermined power is held constant for 11 min in case of ST = 1 (and 5.5 min in case of ST = 1/2). The experiment is designed such that when the battery is not able to deliver the intended power, it goes to rest for a time period of 1 min. Open circuit voltage (OCV) of battery was also monitored over a one-minute rest period after every power step, whether or not the power step was a failure. The OCV data was later used to evaluate the battery efficiency characteristics. Such experiments have been conducted for different scale factors and electrolyte volumes. Results from these simulation runs, together with initial redox flow battery characterization study, are discussed in the next Section 3.
