Performance

The relative accuracy of estimators is difficult to ascertain as much of the error comes from dynamics not modelled by the reference model, and so only show up during experimental testing. The current sensors and cell capacity estimates used for this testing were not sufficiently accurate to be able to use coulomb counting as a reliable metric. As discussed further in Submission 5, it was found in practice that the 3RC estimator performed better than the 1RC version, but still suffered from many of the same issues, notably sensitivity under relaxation and a lack of excitation during constant current operation. SOC estimation accuracy

8 _{A longer time frame could be fitted by downsampling the data. As the focus is on low frequency}

dynamics, downsampling should not affect the parameterisation too much, although it may impact the internal resistance estimate. More research is required to explore this further.

could be inferred from observing how much the estimate changes once a load profile has finished and the cell relaxes, as the voltage correction becomes much stronger (after complete relaxation, the filter will just act like an OCV-SOC lookup table). The estimators appeared to consistently operate with less than 2% error.

4.4 Summary

This section has demonstrated the various uses of ECMs throughout this work. Section 4.1 showed how cells in parallel can be modelled, and that contrary to popular belief, can become significantly imbalanced. Other effects such as differences in current and temperature were also discussed. These have implications for battery pack design as well as imbalance and there is a considerable amount of possible research around this area. Section 4.2 used ECMs in series to analyse imbalance and create a plant model, which is used further in chapters 5 and 6 for developing a balancing control system and perform closed-loop simulations. Cell state estimators were developed in section 4.3 to estimate SOC so that imbalance can be evaluated. These are used in Chapter 6 as part of the real-time experimental set-up. With cell and battery modelling addressed, the next Chapter focuses on modelling and control of the balancing system itself.

5

Balancing System Control

In Chapter 2, a number of conclusions were drawn regarding the requirements of a balancing control system:

• The high-level control goal is to ensure that all of the cells are balanced by EOC and EOD. This allows for all of the energy within the battery pack to be utilised.

• The low-level control goal is to bring all cells to the same SOC. This will generally be the mean SOC, but could also be the maximum or minimum;

• A generic control framework is desirable, as it avoids limiting the control system to one type of hardware.

• This generality means it must be easy to adapt to specific hardware, e.g. factoring in current limits and inter-cell connections.

This Chapter addresses the fourth Research Objective of the EngD: to develop a generic balancing control system with the specific goal of maximising the energy utilisation of the battery pack. A control-oriented model of the cells with respect to the balancing system is derived and used to implement controllers to remove energy imbalance. At this point, a generic, idealised balancing system is considered in order to focus on the more fundamental aspects of the control problem. An implementation with specific hardware is detailed in Chapter 6. The generic system considered for development is shown in Figure 35.

Details about each signal are presented in Table 12, and a description of each subsystem in Table 13. This encapsulates the balancing system itself, along with the other aspects of the battery pack and BMS that are required for balancing.

Table 12: Battery subsystem descriptions

Signal Range Accuracy Description

Cell Voltage 0 to 5V 1mv The voltage values used by the BMS are assumed to be post filtering and processing. Higher accuracy voltage measurements can improve SOC estimation, especially for cells with flat regions in the OCV-SOC curve.

Load Current ±2C 0.1% full scale

The current values used by the BMS are assumed to be post filtering and processing. The specific range and resolution will be dependent on the application and performance specifications. HEVs typically operate at much higher C-rates than a BEV, but the cell capacity is smaller, so the measured current magnitude might be lower.

SOC 0 to

100%

0.5% The SOC estimation accuracy depends on cell

properties and algorithm performance, which in turn is determined by the requirements of the system.

Balancing Current

±0.2C 0.01A The specific range of current is dependent on the application and hardware capability.

Time to

EOD/EOC

0-7200s 60s The remaining mileage/ time remaining is estimated by the energy management system, and sent to the BMS.

Time-to- balance

0-7200s 60s The time-to-balance estimate is calculated by the balancing controller, and can be compared with the time to EOC/EOD to assess whether balancing should be activated.

Balancing Signal

0-1 0.01 Depending on the balancing system interface, cell current may be required to be translated into a normalised value (or some other abstract signal). It will also likely need to be quantised

and transmitted via a digital communications bus such as CAN or SPI.

Balancing Management Signal

Boolean - An overall signal to enable or disable balancing. If disabled, the balancing algorithm should still run in the background to give an up to date time- to-balance.

Table 13: Subsystems relating to cell balancing

Subsystem Description

Battery Pack This contains the cells, balancing hardware, battery management system microcontrollers, safety circuitry and thermal management.

Cells Each series unit of cells requires a voltage measurement. For systems with passive balancing, typically only the applied current is measured but for ABSs, cell current measurements could improve SOC estimation accuracy, though may be inferred from the load and the balancing current calculation.

Temperatures sensors are also positioned throughout the pack (typically less than one sensor per cell). As well as for safety and thermal management, these can also feed into the estimation algorithms for improved accuracy.

State Estimators Estimates of SOC and SOH (cell impedance and capacity) are

required by the BMS. A joint estimator may be used to estimate all signals simultaneously, or SOH may be decoupled from SOC owing to the different timescales.

Balancing Manager

This makes the decision whether balancing should take place, given the status of the cells and the load profile and history. See section 5.1 for details.

Imbalance regulator

This is the core algorithm to determine what balancing current each cell requires based on the cell SOCs. The details of the proposed solutions are in section 5.4.

Hardware Configuration

This translates the balancing current request into a signal required by the balancing hardware. See “Balancing Signal” in Table 12.

Range Estimator An estimate of the remaining driving time/distance of the vehicle is

performed by the energy management system, and is outside of the scope of the balancing system.

The following assumptions are made regarding this generic architecture of the balancing system:

• Every cell can be set to balance, and can be operated simultaneously. If this is not directly feasible (for example, the Texas Instruments EV1401EVM balancing development board [145] can only set one cell to balance per module), the hardware configuration layer could implement multiplexing, which cycles through each cell, setting it to balance for a short period of time.

• There are limits on balancing current magnitude. These are considered here as inequality constraints, but other forms of constraints could also be applied. Each cell can have different current limits, and different values for charging and discharging (by setting one of these to zero, uni-directional balancing can be implemented). These constraints could be a function of operating conditions such as cell voltage, but are considered time-invariant here.

• While SOC is fundamental to the balancing system, the cell state estimators are separate to the balancing controller. The cell SOC estimates are treated as measurements (with some uncertainty) by the balancing controller. The cell capacity estimates from the SOH estimator are also required by the controller. However, these will change slowly (for example, 20% over the course of 5-8 years [146]) and can be assumed as constant during any balancing operation, and periodically updated between balancing.

The high-level strategy for deciding when to balance is proposed in section 5.1. The low-level controller structure is outlined in section 5.2, and the model used to design the controllers derived in section 5.3. The specific controllers for regulating imbalance are derived in section 5.4, based on this model. Simulations are presented in section 5.5, with conclusions drawn in section 5.6. The control system development is primarily covered in Submissions 3 and 5.