The estimation of the state of charge (SOC) of a lithium battery is technically difficult, particularly in applications that don’t fully charge the battery or fully discharge it. Such an application is a hybrid electric vehicle (HEV). The challenge stems from the fact that lithium batteries have a very flat voltage discharge characteristic. There is little change of voltage from a 70% SOC to a 20% SOC. In fact, voltage changes due to temperature change are similar to the change of voltage due to discharge, making it essential to compensate for battery temperature if SOC is to be derived from voltage.
Figure 1: Lithium Battery Gauging
Yet another challenge is the fact that battery capacity is dictated by the capacity of the lowest capacity cell so rather than judge SOC from battery terminal voltage, it should be judged from the terminal voltage of the weakest cell. This is all starting to sound a bit too hard. So why don’t we simply keep a running total of the current going into a battery and balance that with what goes out? This is termed coulomb counting and sounds simple but there are a number of difficulties with this method too.
The difficulties are:
- Batteries are not perfect accumulators. They never give back what you put into them. There is current leakage during charging and the leakage varies with temperature, rate of charge, state of charge and age.
- The capacity of the battery also varies non-linearly with the rate of discharge. The faster the discharge the lower the capacity. The reduction may be as much as 15% from a 0.5C discharge to a 5C discharge.
- Cells have a leakage current which increases substantially at higher temperatures. Inner cells in a battery may well run hotter than outer cells, so cell leakage will be unequal through the battery.
- Capacity is also a function of temperature. Certain lithium chemistries are more affected than others.
- To compensate for this inequality, battery cell balancing is employed within the battery. This additional leakage current is not measurable outside the battery.
- Battery capacity steadily reduces over the life of the battery and with time.
- Any small offsets in current measurement will be integrated and over time can become a large number which seriously affects the accuracy of the SOC.
All the above results in a drift of accuracy over time unless periodic corrections are made but it is only possible to correct when the battery is nearly discharged or nearly full. In HEV applications it is preferable to keep the battery at ~50% charged, so a possible means to reliably correct gauging accuracy would be to periodically fully charge the battery. Pure electric vehicles are periodically charged to full or near full so gauging based on coulomb counting can be quite accurate particularly if other battery issues are compensated.
Key to good accuracy with coulomb counting though is good current sensing over a wide dynamic range.
The traditional approach for measuring current is to us a shunt but these fall down when higher (250A+) currents are involved. Because of power dissipation issues shunts need to be low resistance. Low resistance shunts are not good for measuring low (50mA) currents. This immediately brings up the most important issue: what is the minimum and maximum currents that require measurement? This is termed the dynamic range.
To make a rough estimate of an acceptable integrated error by assuming a 100Ahr battery.
A 4 amp error will generate a 100% error in one day or 0.4A error will generate a 10% error in a day.
A 4/7A error will generate a 100% error in one week or 60mA error will give a 10% error in a week.
A 4/28A error will generate a 100% error in one month or 15mA error will give a 10% error in a month which is probably the best that can be expected of gauging that does not get recalibrated by a charge or a near full discharge.
Let’s now look at a shunt to measure the current. For 250A, a 1m ohm shunt would be on the high side and generate 62.5W. However at 15mA it will only generate 15 microvolts which would be lost in the noise floor. The dynamic range is 250A/15mA = 17,000:1. A 14bit A/D converter would be required if it could actually “see” the signal amongst noise, offsets and drifts. A significant offset cause being thermocouple generated voltages and ground loop shifts.
Fundamentally then, no single sensor will be practical to measure currents with this dynamic range. A high current sensor is required to measure the higher currents from example traction and charging while a low current sensor is required to measure current from for example accessories and any zero current state. Since the low current sensor will also “see” high currents, it must not be damaged or corrupted by these other than to saturate. This immediately counts out shunts.
|Warren Pettigrew is Chief Technical Officer at Raztec (New Zealand) Limited|