# Algorithms

There are a number of fundamental functions that the BMS needs to control and report with the help of algorithms. These include:

• State of Charge (SoC)
• State of Power (SoP)
• State of Capacity (SoQ)
• State of Energy (SoE)
• State of Health (SoH)
• State of Function (SoF)
• State of Resistance (SoR)
• Contactors Control
• Cell Balancing
• RUL Estimation
• Temperature Estimation
• HV Isolation
• Operational Limits Protection
• Diagnostics
• Fallback Modes
• Logging

Therefore there are a number of algorithms required to estimate, compare, publish and control.

### State of Charge

Abbreviated as SoC and defined as the amount of charge in the cell as a percentage compared to the nominal capacity of the cell in Ah.

#### SoC Estimation Techniques

A look at the estimation of State of Charge (SoC) using voltage profiling and coulomb counting. These two methods give a good overview of the difficulty and errors associated in estimating this critical battery parameter.

## State of Capacity

The State of Capacity (SoQ) is defined as the amount of electrical charge that can be held by each cell. It usually is defined using the Ah (Ampere-hour) unit, which is just a factor of As (Ampere-second), which is equivalent to C (Coulomb), the SI unit for electric charge.

This parameter can be estimated as defined in the equation below.

The goal is to integrate the current over time to find out how much charge the cell output in this defined time window. Then, divide by the SoC delta over the same period of time. Hence, by its nature, it is an opportunistic measurement that can only be estimated over regular charge or discharge cycles (i.e. cannot be estimated continuously).

### State of Health

The SoH of the cell is the total available charge capacity of the cell as a percentage compared to the nominal capacity in Ah when the cell was new.

Mileage equals Wear – a discussion around the spread in SoH data from real users and some of the factors that impact it.

### State of Power

#### Current Limit Estimation

There are a number of reasons to estimate the charge and discharge current limits of a battery pack in real time:

• adhere to current safety limits of the cells
• adhere to current limits of all components in the battery pack
• avoid sudden loss of power or even a need to shutdown

## State of Energy

The State of Energy (SoE) refers to the amount of usable energy stored in each cell. The amount of usable energy contained in all the cells of the pack will determine how much energy can be spent, and therefore, how much range you have left in your electric vehicle.

This estimate is proportional to the SoC and SoQ, as seen in the equation below.

You can also calculate how much energy left you have in percentual terms using the following two equations.

## State of Resistance

The State of Resistance (SoR) is an attempt to model the ohmic losses of a cell during its operation. This is an important parameter to some more advanced SoX estimation algorithms. A rough estimation can be derived from a well known equation:

## Contactors Control

It is not so simple to manage a battery pack’s contactor

### Cell Temperature

Very rarely do you measure the temperature of every cell in a battery pack, however, you do need to operate the pack within the limits and apply these limits to every cell. This means you need good estimation techniques that take into account:

• charge / discharge power
• cooling system design and operating parameters
• cell to cell system environment differences
• cell design
• environment inputs / outputs

This is just a starter, you also need to understand how the system will age and how the measurement system works. Algorithms are key are factor of BMS.

#### Cell Temperature Sensing

• Hard Sensors
• Contact
• Thermocouples
• Thermistors
• Resistance Temperature Detectors
• Optical Fibre Sensors
• Contactless
• Electrochemical Impedance Spectroscopy
• Johnson Noise Thermometry
• Infrared Laser Thermometer
• Soft Sensors
• Mathematical Model Based Estimators
• Bulk Internal Temperature Estimators
• Distributed Internal Temperature Estimators
• Hybrid Model Based Estimators

### HV Isolation

It is really important to understand that 500Ω/V is a legislative requirement for the vehicle. Which means it applies to the whole HV system not just the battery – a common misunderstanding. Several things follow from this:

1. The isolation monitoring system must be capable of measuring the isolation impedance of the whole HV system
2. The isolation resistance target for each individual component in the system, including the battery, needs to be allocated by the systems engineering team as a vehicle specific requirement
3. Legislatively the system isolation resistance only needs to be measured when the HV system is on, which is when HV is present. There is no HV system level requirement for the battery to measure its own resistance when the contactors are open.
4. If the vehicle is a hybrid or plug in hybrid then it is possible for the HV system to have HV present even if the contactors are open. There are several operating scenarios where this is desirable e.g. the battery is too cold.
5. From the above, the best place to measure the HV system isolation resistance is at the HV Bus side of the contactors and the monitor has to work when the contactors are open.