Comparison

As noted, the balancing time for pole placement is slow, with the remaining three controllers all balancing in similar times. In reality, the amount of energy loss will be heavily dependent on the specific hardware used. For this generic system, it is assumed there are two components to the losses. There is a transformer efficiency which causes a power loss Pc, (77), and resistive losses Ps, given by (78). The transformer efficiency ηtf is assumed to be 95%, and the effective transformer resistance Rtf is set as 0.6Ω, which was chosen to give a total efficiency of 80% at maximum current.

𝑃` = Ï1 −𝜂cêÐ𝑖'ar𝑣c (77)

𝑃_o = 𝑖_'arˆ _𝑅

cê (78)

The energy usage for the four controllers implemented here are given by Table 16. As expected, the rule based system has consumed the most energy, with the feed-forward control approach only dissipating 78% as much energy. Pole placement used more energy despite operating a low currents, because of the longer balancing time. The energy wasted by the rule-based system is 9.88% of the total energy remaining in the cells at the start of the simulation, compared to

7.78% for the feed-forward controller. This allows for over 2% greater energy extraction, while is the ultimate aim of the balancing controller, and important considering how important relatively small gains in energy utilisation can be when a battery pack is operating across its full SOC window.

Table 16: Energy loss during balancing simulations Balancing Energy Loss (J)

Cell Rule-based PP MPC Linear

1 2187.1 3311.8 2301 2942.7 2 1492.1 2082.6 1210.7 1849.5 3 2212.5 1659.1 2100.4 1472 4 2136.3 1571.3 2023 1394.2 5 1542.9 898.76 1428.8 797.57 6 1438.4 781.98 1325.7 693.97 7 1230.7 548.68 1119.3 486.94 Total 12240 10854 11509 9637 5.6 Summary

This section has outlined a means of controlling a generic balancing system based on cell SOC knowledge. The control model is linear and only dependent on one parameter (cell discharge capacity) per cell. Using cell capacity adds knowledge of whether the cell SOCs will naturally diverge or converge owing to the applied load. A large battery pack may not transfer energy from all cells, and instead by split into submodules of a few cells. The interaction matrix F was introduced to specify which cells connect to which.

The model has been used to create three different controllers, in addition to a non-model based controller. The results presented in section 5.5 show that pole placement takes a long time to balance and results in a steady-state error. This is at odds with the requirements of an effective balancing system: to balance fast and minimise the final SOC difference. The DSIC was derived which has target of removing the most amount of imbalance, while ensuring better convergence of balancing times. This avoids bringing some cells to the mean before others, at which point there will be extra switching on those cells as they are maintained at the mean. The feed-forward controller has the express aim of ensuring the cells reach EOB simultaneously, and was shown to use the least energy. Furthermore,

it has a slightly longer balancing time than the rule-based and DSIC approaches, but the fastest possible balancing is not crucial to performance: there is a compromise between time and wasted energy.

It is possible to refine the DSIC and feed-forward approaches to increase balancing time without significantly increasing energy usage. There are also more control methods which were not explored. For example, sliding mode control [159] could be effective, but was not considered here because of the considerable amount of design work required and implementation challenges with respect to “chattering” – continual oscillations about the target.

The purpose of this Chapter was to meet Research Objective 4: the design of a generic balancing control system. Many controllers were considered, and three have been described in detail and simulated to compare performance. This leads into the experimental work defined by Research Objective 5. For these controllers to be validated, they need to be applied to a specific ABS. The hardware used to do this, and the experimental results, are detailed in the next Chapter.

6

Hardware Implementation

The control framework in Chapter 5 was designed considering a non-specific balancing system. As per Research Objective 4, this was to demonstrate how a common model can be applied to a wide variety of balancing hardware, rather than becoming obsolete when the hardware changes or is updated. However, to validate the proposed control solution it is essential to demonstrate that the control system can be implemented with specific hardware, which is why Research Objective 5 was proposed. As well as testing the controller, this was also an opportunity to evaluate third-party hardware in more detail and from this learning experience produce recommendations for future balancing equipment. Finally, it meant implementing the control system in real-time subject to imperfect measurements and SOC estimation errors. This brings the research back up the systems engineering “V” in Figure 3. Using these experimental results, Research Question 2 can be answered by using the experimental results to quantify the benefits of active balancing.

Some issues with the experimental equipment are first highlighted in section 6.1. The balancing hardware used for this test work is described in section 6.2, followed by the instrumentation required to evaluate and monitor the system in section 6.3 and the load to apply a current to the series string of cells in section 6.4. The control system implementation and interfacing with the hardware is discussed in section 6.5. The balancing system is evaluated in section 6.6, and then the closed loop balancing test results presented and discussed in 6.7. Simulation studies to complement these results are contained in section 6.8, and the total system performance is analysed in section 6.9. Based on this test work, recommendations for hardware design and specification are detailed in section 6.10, followed by a summary of the Chapter in 6.11.