The technical issues with, and eventual failure of, the balancing hardware meant that it was not possible to perform a single comprehensive set of tests with a completely consistent of experimental conditions. A summary of the tests performed is given in Table 22. The Artemis Combined drive cycle was chosen to act as a representative vehicle load, as it contains a wide range of vehicle operating modes and so varied current excitation. A standard vehicle model developed within Catapult [143] was used to convert the Artemis speed profile into a battery current profile.
Table 22: Summary of experimental test conditions
Test Controller Drive
Cycle
Cells Used
Estimator Duty Cycle Calculation Comments 1 Pole Placement None 2,3,5,6 1RC CDKF Average - 2 Pole placement Artemis (15A peak) 2,3,5,6 1RC CDKF
Optimisation The cell 6 current sensor saturated at 12A 3 DSIC Artemis (20A peak) 2,3,6,7 CDKF With NLLS
Optimisation Balancing currents for cells 6 and 7 were lower than usual because of a short circuit
6.7.1 Pole placement
Figure 64 shows the cell SOCs and absolute (maximum minus minimum) SOC difference for the pole placement controller with no external load. The circles at the start and end of the SOC plot give the SOCs obtained from using the OCV- SOC with the relaxed cell voltages. This is used to indicate if the estimators are performing poorly. The SOC estimation results are particularly accurate for this test for two reasons. Firstly, there is no external load, the cells are only subject to low currents which affect the cell terminal voltage by a few millivolts. Secondly, duty cycling means that some or all the cells will be undergoing no current (or very low feedback currents) for part of each one second window. This short excitation followed by a rest means the cells are at an almost relaxed state for part of the time – particularly towards the end of balancing when the duty cycles are small. Both of these factors result in strong voltage correction from the estimator. At the end of the test, the mean difference between the estimated and measured SOCs was 0.01% SOC.
Figure 64: SOC and duty cycle results for pole placement under no load
For this test the closed-loop pole obtained using bisection was -6.06e-4 which equates to a time constant of 1650 seconds. The results show that stable
imbalance removal was achieved in line with the exponential response of a state feedback controller. The absolute imbalance started at 4.1% and was reduced to 0.14% by the end of the experiment. As expected with state feedback, the majority of the imbalance reduction takes place early on in the test. The lower plot shows that absolute imbalance which reduced to 1% after 1650 seconds. This means that the balancing system is on for a long time which, on board a vehicle, would increase the charge lost due to standby power draw, and is not as effective when imbalance has to be reduced in a short period of time.
The same pole placement controller was then applied with a discharging Artemis Combined drive cycle. The drive cycle was repeated until the cell SOCs became relatively low, at which point the balancing system stopped functioning as discussed in section 6.1. The cell currents and resultant SOC estimates are shown in Figure 65.
Figure 65: Cell currents and SOCs for pole placement under Artemis Combined drive cycle They show the periodic discharging profile as the cells discharge from around 92% SOC to 14% SOC. Figure 66 shows the SOC imbalance results. The
uncertainty, the controller not factoring in the load current, and saturation of some of the duty cycles. Despite this, the imbalance is reduced significantly by 30 minutes. After this point, the controller would ideally operate as a regulator reacting to the drive cycle disturbance. This is achieved to some extent, but there are several periods during which imbalance increases. This is typically during the high-current region of the input profile: the 60-75 minute, 100-115 minute and 140-155 minute regions. This apparent increase in imbalance arises from SOC estimation error. The nature of the experiment means there is no baseline reference to observe how accurate the SOC estimation is apart from before and after the test. However, there are two observations on estimator performance. Firstly, after this part of the drive cycle there is a rest period, which should allow the estimator to converge on the ‘true’ SOC (from the OCV-SOC curve) as the cell relaxes. Secondly, the SOC estimates generally increase during this convergence period, implying that the estimates have been too low during the previous discharging phase.
Pole placement can be slow to respond to these increases in imbalance. As mentioned above for the no load case, performance could be improved by retuning the controller. Given that there may be continual and unexpected changes to the SOC estimates, the controller should respond to them quickly because the uncertainty is not known in the future. A slow response increases the chances that the controller will not be able to reduce imbalance before the cells reach EOC/EOD. As discussed in Chapter 5, while the above pole placement algorithm could be improved to speed up this imbalance response, its fundamental operation is not well suited to fast imbalance removal.
6.7.2 DSIC
To validate the performance of the DSIC algorithm, the same Artemis profile was applied as for the pole placement tests, but starting from around 60% SOC with a larger initial imbalance. The current and SOC results are shown in Figure 67, and the relative and absolute SOC differences shown in Figure 68. The drive cycle is scaled to a higher maximum value (20A rather than 15A).
Figure 68: ΔSOC and absolute SOC difference for DSIC under Artemis Combined drive cycle The results show that the controller can quickly reduce the SOC difference, and maintain a low difference over the drive cycle. This quadratic controller is quicker to returned the system to a balanced state in the event of a disturbance such as SOC estimations correcting during cell relaxation. In this sense, the DSIC approach effectively acts as a better regulator than pole placement in the face of the various sources of uncertainty.