State of charge and state of health
State of charge (SoC) of a lead-acid battery, expressed in %, is the ratio of the remaining capacity (RC) to the full charge capacity (FCC) (see Fig. 1). FCC is the usable capacity at the present charge or discharge rate and temperature. FCC is derived from battery full chemical capacity (QMAX) and battery impedance (RBAT) (See Fig. 2). For example, for a new lead-acid battery of 100 Ah design capacity, when it is fully charged, the SoC is 100% since the FCC is 100 Ah and RC is also 100 Ah. If that new battery is discharged so that RC is 70 Ah, then the SoC is 70%. As the battery ages, its full chemical capacity (QMAX) tends to be lower than the design capacity due to chemical degradation. SoH monitors this chemical degradation and is reported in % as the ratio of the FCCH to the design capacity, where FCCH is FCC at 25°C for design charge or discharge rate (Fig. 1). For example, if the battery with design capacity of 100 Ah has a FCCH of only 85 Ah after one year in use, then its SoH is 85%. In short, SoC indicates how much charge is left before a recharge is needed, while SoH indicates when a battery will have to be replaced.
Fig. 1: How SoC, SoH, QMAX and RBAT of a battery are calculated
Fig. 2: Full charge capacity (FCC) is derived from QMAX and battery impedance RBAT
Limitations of using terminal voltage for SoC
While it is easy to measure and monitor the battery terminal voltage, unfortunately, this is not a true indicator of the battery’s SoC and SoH, due to the effects of charge/discharge current and temperature. The biggest impact comes from the chemical kinetics during charge and discharge of the battery. To get a reasonable estimate of the SoC from voltage measurement, the battery needs to rest for at least few hours (for example, four hours) to attain equilibrium before the open circuit voltage (OCV), in other words, no-load voltage, can be measured. See Table 1 for the Battery Council International (BCI) recommended values for a 12-V lead-acid starter battery . While an approximate SoC can be assessed at rest state, it is not possible to continuously assess it during charge and discharge by voltage measurement. Also, it is not possible to assess SoH with just terminal voltage measurement since it does not fully reflect the impact from battery aging. Measuring specific gravity (SG) of the battery electrolyte is another approximation method that is applicable to the flooded lead-acid battery type. But this method also suffers from lack of SoH information, from limitations due to temperature effects, stratified electrolyte concentration, and from the need for the electrolyte to stabilize before taking the SG reading.
Table 1: BCI standard for SoC estimation of a starter battery with antimony. Readings taken at 26°C and battery rested for 24 hours after charge or discharge. 
Given the limitations of the above methods, there is a need for a battery management system (BMS) solution that can automatically make the required measurements and report both SoC and SoH accurately. The latest lead-acid gas gauge, uses Impedance Track gauging technology to accurately monitor and report SoC and SoH of the battery .
Accurately monitoring SoC and SoH
Both SoC and SoH of the battery can be monitored by accurately measuring: battery voltage, battery temperature, and the charge into and out of the battery. When the battery is in rest mode and when the current is below a user chosen threshold, the SoC is determined using the measured battery voltage and a predefined OCV to SoC relationship table that is temperature compensated and unique to that battery type and chemistry . During charge and discharge, the SoC is continuously calculated using FCC and RC while the SoH is calculated using FCCH and design capacity.
Both the SoC and SoH calculations depend on an accurate estimate of QMAX and battery impedance (RBAT). QMAX is estimated when the battery is in the rest state. The corresponding equation is QMAX = QPASSED / (SoC1 – SoC2), where QPASSED is the passed charge between SoC1 and SoC2, and SoC1 is fully rested SoC before charge/discharge activity and SoC2 is fully rested SoC after charge/discharge activity (Fig. 3). Once the QMAX is calculated, the same value is used to calculate SoC and SoH during charge/discharge state until the next QMAX update is done. Similarly, RBAT is estimated using the equation RBAT = (V–OCV) / I, where V is battery voltage, OCV is the open circuit voltage, and I is charge/discharge current. As the battery ages, its QMAX drops and RBAT increases. The Impedance Track algorithm tracks both to accurately report SoC and SoH.
Fig. 3: QMAX depends on SoC at rest before and after a charge (or discharge) and the Passed Charge QPASSED
By monitoring SoC and SoH of the lead-acid battery using Impedance Track gauging, it is possible to provide a better user experience by continuously and accurately reporting the remaining charge, and also by cautioning when a battery needs to be replaced. This also helps to avoid loss of server data, a wireless outage, or a stranded passenger.
The downsides of Lead Acid batteries
1/ Limited “Useable” Capacity
It is typically considered wise to use just 30% – 50% of the rated capacity of typical lead acid “Deep Cycle” batteries. This means that a 600 amp hour battery bank in practice only provides, at best, 300 amp hours of real capacity.
If you even occasionally drain the batteries more than this their life will be drastically cut short.
2/ Limited Cycle Life
Even if you are going easy on your batteries and are careful to never overly drain them, even the best deep cycle lead acid batteries are typically only good for 500-1000 cycles. If you are frequently tapping into your battery bank, this could mean that your batteries may need replacement after less than 2 years use.
Fig. 4.Lead-acid(AGM) expected Life Cycles
3/ Slow & Inefficient Charging
The final 20% of lead acid battery capacity can not be “fast” charged. The first 80% can be “Bulk Charged” by a smart three-stage charger quickly (particularly AGM batteries can handle a high bulk charging current), but then the “Absorption” phase begins and the charging current drops off dramatically.
Just like a software development project, the final 20% of the work can end up taking 80% of the time.
This isn’t a big deal if you are charging plugged in overnight, but it is a huge issue if you have to leave your generator running for hours (which can be rather noisy and expensive to run). And if you are depending on solar and the sun sets before that final 20% has been topped off, you can easily end up with batteries that never actually get fully charged.
Not fully charging the final few percent would not be much of a problem in practice, if it wasn’t for the fact that a failure to regularly fully charge lead acid batteries prematurely ages them.
4/ Wasted Energy
In addition to all that wasted generator time, lead acid batteries suffer another efficiency issue – they waste as much as 15% of the energy put into them via inherent charging inefficiency. So if you provide 100 amps of power, you’ve only storing 85 amp hours.
This can be especially frustrating when charging via solar, when you are trying to squeeze as much efficiency out of every amp as possible before the sun goes down or gets covered up by clouds.
5/ Wasted Energy
Flooded lead acid batteries release noxious acidic gas while they are charging, and must be contained in a sealed battery box that is vented to the outside. They also must be stored upright, to avoid battery acid spills.
AGM batteries do not have these constraints, and can be placed in unventilated areas – even inside your living space. This is one of the reasons that AGM batteries have become so popular with sailors.
6/ Maintenance Requirements
Flooded lead acid batteries must be periodically topped off with distilled water, which can be a cumbersome maintenance chore if your battery bays are difficult to get to.
AGM and gel cells though are truly maintenance free. Being maintenance free comes with a downside though – a flooded cell battery that is accidentally overcharged can often be salvaged by replacing the water that boiled off. A gel or AGM battery that is overcharged is often irreversibly destroyed.
7/ Peukert’s Losses & Voltage Sag
A fully charged 12-volt lead acid battery starts off around 12.8 volts, but as it is drained the voltage drops steadily. The voltage drops below 12 volts when the battery still has 35% of its total capacity remaining, but some electronics may fail to operate with less than a full 12 volt supply. This “sag” effect can also lead to lights dimming.
Fig.5 Lead-acid AGM discharge curves
Also – the faster that you discharge a lead acid battery of any type, the less energy you can get out of it. This effect can be calculated by applying Peukert’s Law (named after German scientist W. Peukert), and in practice this means that high current loads like an air conditioner, a microwave or an induction cooktop can result in a lead acid battery bank being able to actually deliver as little as 60% of its normal capacity. This is a huge loss in capacity when you need it most…
8/ Size & Weight
A typical 8D sized battery that is commonly used for large battery banks is 20.5″ x 10.5″ x 9.5″. To pick a specific 8D example, Trojan’s-AGM weighs 167lbs, and provides just 230 amp-hours of total capacity – which leaves you with 115 amp hours truly usable, and only 70 for a high discharge applications!
If you are designing for extensive boon docking, you will want at least four 8D’s, or as many as eight. That is a LOT of weight to be carting around that impacts your fuel economy.
And, if you have limited space for batteries on your rig – size alone of the batteries will limit your capacity.
Fig. 6, Specific energy density by battery technology