As with the wind turbine model, new components of the flow battery model have been validated. Bindner et al. [137] have conducted an extensive long-term practical evaluation of a small scale (15kW, 120kWh) VRFB by Prudent Energy and published significant results. Some of the key results presented there are used to validate the VRFB model developed here. As the VRFB systems are modular systems, relying on modules of this size to build larger systems, validation of the electrochemical stacks model against this data gives a good approximation to likely performance of much larger systems.
6.4.1 Software
The flow battery model has been implemented in both DIgSILENT PowerFactory and Matlab-Simulink. The Matlab-Simulink model is better suited to modification and tuning of the power converter and state of charge control loops, however, it is too slow to allow long time scale studies with a high energy capacity VRFB. As an alternative, the model has also been implemented in DIgSILENT PowerFactory which allows longer time-scale studies and ready integration with the earlier developed model of a wind turbine to represent a complete wind farm with energy storage. The model outputs have been
400k 33kV 690V Transmission Grid IGBT SVC and VRFB 132k 33kV Wind Turbine Model Offshore Cable 690V 132k 33kV Collector Cable
compared to confirm that they match and the validation plots shown here are from the DIgSILENT model.
6.4.2 Flow Battery Voltage
145 150 155 160 165 170 175 180 185 190 -40 -20 0 20 40 60 80 100 120 State of Charge (%) E M F ( V )
Figure 6.8: VRFB Voltage according to Bindner et al. [137] (Top) and Model (Bottom)
Figure 6.8 shows the DC open circuit voltage across the VRFB at various different state of charge levels. The top plot shows the reported results from Bindner et al. The maximum and minimum states of charge (SOC) reported here are outside of the nominal operating range (<0% and >100%) representing a load level beyond that of the battery’s normal operational limits. Bindner et al. state that this is due to the difference between the SOC
reported by the battery (which is an interpolation of various data points and is shown in the plot) and the theoretical state of charge as calculated from the state of the battery. The application of the VRFB to providing frequency response services with a wind farm is likely to involve repeated charge and discharge cycles, as such; it is not acceptable to allow the state of charge of the flow battery to exceed the nominal operating range as this would rapidly degrade the VRFB’s lifetime. Furthermore, as the voltage drops, the constant power current increases, hence at low states of charge the current for rated power would be at a maximum. The power converter would be optimally sized for rated power capacity at the lowest nominal state of charge; hence, at the low end of the range the power converter’s current limit would lead to reduced output power. Hence, the battery’s reported state of charge would be used in order to ensure operation within the designed limits of SOC. This means that the model needs only replicate the voltage profile in the nominal state of charge operating range and not the extended range.
As a result of some of the underlying assumptions in simplifying the VRFB model, the physical molar concentrations of Vanadium ions do not directly correspond to the concentrations applied in the Nernst equation to calculate the open circuit potential. As a result, the five underlying concentrations (four Vanadium ion concentrations and the acid concentration) have been tuned to optimise the match between the VRFB output and the model output; this is a quick manual process that only affects the initial concentrations and not the magnitude of changes in concentration of the various ions. Figure 6.8 shows the result of a tuned electrochemical model across the normal state of charge range for the VRFB. The validation plot shows that the slight non-linearity in the voltage profile has been replicated and that at all states of charge the open circuit voltage is well within 3% of the expected value and is normally within 1.5%.
This voltage to state of charge profile also highlights the current output variation that can be expected from the VRFB. As the power converter will operate to ensure that the battery provides a constant power output, the boost converter current will increase by more than 10% as the battery state of charge drops from its rated level.
The non-linearity in the voltage profile also helps to show the benefits of a limited operating range. As the SoC approaches full charge, the voltage increases more steeply, hence the power converter voltage rating would have to increase significantly to provide a limited additional capacity for operation at higher states of charge. Conversely, as the SoC reaches the lowest nominal level, the voltage drops more severely, indicating that the power converter’s current rating would have to increase substantially to provide limited
additional power capacity from lower states of charge. Overall, the optimal system will be developed and the model agreement has been shown to be acceptable based on less than 3% difference in the model and output voltage across the entire operating range.
6.4.3 Round Trip Efficiency
0 10 20 30 40 50 60 70 80 90 100 0.0 20.0 40.0 60.0 80.0 100.0 Power (% of Capacity) R o u n d T ri p E ff ic ie n c y ( % ) VRFB Stacks Full System
Figure 6.9: Energy Store System Round Trip Efficiency according to Binder et al. [137] (Top) and Model (Bottom)
The top plot in Figure 6.9 shows the practical efficiencies achieved with constant power charge and discharge cycles. The two plots’ x axes have been approximately aligned to allow quicker cross referencing. The gold coloured plot shows the round trip efficiency from the electrochemical part of the flow battery system (stacks, membrane and stack concentration changes). This agrees well with the modelled round trip efficiency, shown
by the blue line in the lower plot. This validates the efficiency of the electrochemical part of the model.
Bindner et al. noted the low efficiency of the power converter in their installation (<85% round trip). This in part is due to its smaller scale (15kW) when compared to the systems typically supplied for commercial applications. However, their power converter also suffered very poor response times, suggesting that the design was poor. Furthermore, the total auxiliary load on the 15kW system represented a higher proportion of rated output than would be the case for a larger scale system. As a result the electrical model represents the typical commercial system, with the ancillary load set according to that experienced for real applications where the load was approximately 1/6th of the rated power. This leads to a higher round trip efficiency for the full system model of a large scale VRFB (lower plot, magenta) than the measured round trip efficiency on the small scale demonstrator (top plot, blue). This is in line with claims that the efficiency of VRFB systems will improve with scale but is still lower than the average 70-85% range projected in Table 5.18, which is the range widely predicted in the literature.
The overall round-trip efficiency plot illustrates the need to consider the dynamic efficiency. The non-linearity in efficiency means that in a real world application, particularly in conjunction with an intermittent resource such as wind power, the instantaneous losses will vary widely. Overall, this representation of round trip efficiency will provide an accurate projection of likely VRFB commercial performance.