Estimation of the state of charge (SOC) of a lithium battery is technically difficult, especially in applications where the battery is not fully charged or fully discharged. Such applications are hybrid electric vehicles (HEVs). The challenge stems from the very flat voltage discharge characteristics of lithium batteries. The voltage hardly changes from 70% SOC to 20% SOC. In fact, the voltage variation due to temperature changes is similar to the voltage variation due to discharge, so if the SOC is to be derived from the voltage, the cell temperature must be compensated for.
Another challenge is that the battery capacity is determined by the capacity of the lowest capacity cell, so the SOC should not be judged based on the terminal voltage of the cell, but on the terminal voltage of the weakest cell. This all sounds a little too difficult. So why don't we simply keep the total amount of current flowing into the cell and balance it with the current flowing out? This is known as coulometric counting and sounds simple enough, but there are many difficulties with this method.
Batteries are not perfect batteries. They never return what you put into them. There is leakage current during charging, which varies with temperature, charge rate, state of charge and ageing.
The capacity of a battery also varies non-linearly with the rate of discharge. The faster the discharge, the lower the capacity. From a 0.5C discharge to a 5C discharge, the reduction can be as high as 15%.
Batteries have a significantly higher leakage current at higher temperatures. The internal cells in a battery may run hotter than the external cells, so the cell leakage through the battery will be unequal.
Capacity is also a function of temperature. Some lithium chemicals are affected more than others.
To compensate for this inequality, cell balancing is used within the battery. This additional leakage current is not measurable outside the battery.
The battery capacity decreases steadily over the life of the cell and over time.
Any small offset in the current measurement will be integrated and over time may become a large number, seriously affecting the accuracy of the SOC.
All of the above will result in a drift in accuracy over time unless regular calibration is carried out, but this is only possible when the battery is almost discharged or nearly full. In HEV applications it is best to keep the battery at approximately 50% charge, so one possible way of reliably correcting the metering accuracy is to periodically charge the battery fully. Pure electric vehicles are regularly charged to full or nearly full, so metering based on coulometric counts can be very accurate, especially if other battery problems are compensated for.
The key to good accuracy in coulometric counting is good current detection over a wide dynamic range.
The traditional method of measuring current is for us a shunt, but these methods fall down when higher (250A+) currents are involved. Due to the power consumption, the shunt needs to be of low resistance. Low resistance shunts are not suitable for measuring low (50mA) currents. This immediately raises the most important question: what are the minimum and maximum currents to be measured? This is called the dynamic range.
Assuming a battery capacity of 100Ahr, a rough estimate of the acceptable integration error.
A 4 Amp error will produce 100% of errors in a day or a 0.4A error will produce 10% of errors in a day.
A 4/7A error will produce 100% of errors within a week or a 60mA error will produce 10% of errors within a week.
A 4/28A error will produce a 100% error in a month or a 15mA error will produce a 10% error in a month, which is probably the best measurement that can be expected without recalibration due to charging or near complete discharge.
Now let's look at the shunt that measures the current. For 250A, a 1m ohm shunt will be on the high side and produce 62.5W. However, at 15mA it will only produce 15 microvolts, which will be lost in the background noise. The dynamic range is 250A/15mA = 17,000:1. If a 14-bit A/D converter can really "see" the signal in noise, offset and drift, then a 14-bit A/D converter is required. An important cause of offset is the voltage and ground loop offset generated by the thermocouple.
Fundamentally, there is no sensor that can measure current in this dynamic range. High current sensors are needed to measure the higher currents from traction and charging examples, while low current sensors are needed to measure currents from, for example, accessories and any zero current state. Since the low current sensor also "sees" the high current, it cannot be damaged or corrupted by these, except for saturation. This immediately calculates the shunt current.
A solution
A very suitable family of sensors are open loop Hall effect current sensors. These devices will not be damaged by high currents and Raztec has developed a sensor range which can actually measure currents in the milliamp range through a single conductor. a transfer function of 100mV/AT is practical, so a 15mA current will produce a usable 1.5mV. by using the best available core material, very low remanence in the single milliamp range can also be achieved. At 100mV/AT, saturation will occur above 25 Amps. The lower programming gain of course allows for higher currents.
High currents are measured using conventional high current sensors. Switching from one sensor to another requires simple logic.
Raztec's new range of coreless sensors are an excellent choice for high current sensors. These devices offer excellent linearity, stability and zero hysteresis. They are easily adaptable to a wide range of mechanical configurations and current ranges. These devices are made practical by the use of a new generation of magnetic field sensors with excellent performance.
Both sensor types remain beneficial for managing signal-to-noise ratios with the very high dynamic range of currents required.
However, extreme accuracy would be redundant as the battery itself is not an accurate coulomb counter. An error of 5% between charge and discharge is typical for batteries where further inconsistencies exist. With this in mind, a relatively simple technique using a basic battery model can be used. The model can include no-load terminal voltage versus capacity, charge voltage versus capacity, discharge and charge resistances which can be modified with capacity and charge/discharge cycles. Suitable measured voltage time constants need to be established to accommodate the depletion and recovery voltage time constants.
A significant advantage of good quality lithium batteries is that they lose very little capacity at high discharge rates. This fact simplifies calculations. They also have a very low leakage current. System leakage may be higher.
This technique enables state of charge estimation within a few percentage points of the actual remaining capacity after establishing the appropriate parameters, without the need for coulomb counting. The battery becomes a coulomb counter.
Error sources within the current sensor
As mentioned above, the offset error is critical to the coulometric count and provision should be made within the SOC monitor to calibrate the sensor offset to zero under zero current conditions. This is normally only feasible during factory installation. However, systems may exist that determine zero current and therefore allow automatic recalibration of the offset. This is an ideal situation as drift can be accommodated.
Unfortunately, all sensor technologies produce thermal offset drift, and current sensors are no exception. We can now see that this is a critical quality. By using quality components and careful design at Raztec, we have developed a range of thermally stable current sensors with a drift range of <0.25mA/K. For a temperature change of 20K, this can produce a maximum error of 5mA.
Another common source of error in current sensors incorporating a magnetic circuit is the hysteresis error caused by remanent magnetism. This is often up to 400mA, which makes such sensors unsuitable for battery monitoring. By selecting the best magnetic material, Raztec has reduced this quality to 20mA and this error has actually reduced over time. If less error is required, demagnetisation is possible, but adds considerable complexity.
A smaller error is the drift of the transfer function calibration with temperature, but for mass sensors this effect is much smaller than the drift of the cell performance with temperature.
The best approach to SOC estimation is to use a combination of techniques such as stable no-load voltages, cell voltages compensated by IXR, coulometric counts and temperature compensation of parameters. For example, long-term integration errors can be ignored by estimating the SOC for no-load or low-load battery voltages.
Post time: Aug-09-2022