A basic equivalent circuit of the lead-acid battery is modeled by a voltage source with an equilibrium voltage (VE) in series with an internal resistor (Rin)(see fig.1). It must be noted here that this configuration can describe only a current state because the magnitude of VE and Rin are not actually constant, but is function of many parameters such as state of charge (SOC), temperature, current density, and aging of the battery.
Fig.1. Basic equivalent circuit of the lead-acid battery for a current state
Furthermore, it is to consider that these parameters depend also on the current direction (charging or discharge). When the battery were at rest or under open-circuit condition VB = VE. When current is drawn from the battery, the voltage will be lower than VE. When current is flowing into the battery, the terminal voltage will be higher than VE. For example, at each moment during discharge phase the terminal voltage can be derived as follow:
- VbÂ = Ve â€“ VinÂ Â Â Â Â Â //Â Â = Ve â€“ R in Ib Â Â Â Â Â Â Â Â Â
- Vb = terminal voltage [V]
- Ve = equilibrium voltage [V]
- Vin = internal loss voltage [V]
- Rin = internal resistance [W]
- Ib = discharge current [A]
Obviously, higher discharge current results in reduction of the terminal voltage. Therefore, to specify the state of the battery by the battery voltage, discharge current should be also measured.
In case of discharge, the minimum voltage level acceptable for a lead-acid battery is defined as discharge voltage threshold. Falling below this threshold is called deep discharge, with which the battery may suffer damage. In case that the battery is left longer after deep discharge, lead of the support structure is converted to lead-sulphate in rough-crystalline form, which during charging can be only bad or cannot be converted again anymore. As a result, the battery loses a part of its storage capacity; besides loss of support structure arises as well.
In practice, harmful deep discharge is to be prevented: the loads will be compulsory disconnected from battery as soon as the discharge voltage threshold is reached i.e. with the help of a so-called deep discharge protection (DDP). This threshold is basically given in the data sheets by the manufacturer for different discharge currents. Preferably, the value of this threshold should depend on the discharge current. The relation between the discharge current and the voltage during discharge for the lead-acid battery is presented in fig.2.
Fig.2. Discharge characteristic curves
Fig.2 shows the discharge profile of a typical battery type at several constant current rates. The typical end-of-discharge voltage at these discharge rates can also be noticed where the voltage starts to drop steeply. Moreover, the end-of-discharge voltage varies between 1.75-1.9 V, depending on the battery type and the discharge current. Higher service capacity is obtained at the lower discharge rates. At higher discharge rates, the electrolyte in the pore structure of the plate becomes depleted, and it cannot diffuse rapidly enough to maintain the cell voltage. However, intermittent discharge, which allows time for electrolyte diffusion will improve the performance under high discharge rates.
With 2.3 V â€“ 2.4 V, namely the so-called Gassing Voltage, gas is developed at the electrodes in the battery, by which the water is decomposed into hydrogen and oxygen. Both gases mix together in the battery providing detonating gas (explosive!) and escape through ventilation opening in the vent plug. With the gassing, the battery loses also water, which must be refilled according to maintenance within regular intervals. The gas is the unwelcome secondary reaction of the chemical conversion during charging because current is consumed for the electrolysis and therefore the storage efficiency of the battery is made worse unnecessarily. After the gassing voltage is exceeded, voltage stays approximately constant. The whole charging current during this period results in H2 and O2, which is defined as loss.
Freezing of electrolyte
For applications with low ambient temperature, the lead-acid battery must also be protected against freezing of electrolyte. The risk of freezing depends on the state of charge.
Fig.3 illustrates the freezing limit as a function of the state of charge.
Fig.3. Freezing limit of a lead-acid battery dependent on the state of charge
Cycle life of lead-acid batteries
The cycle life refers to a capability of the battery to withstand a certain number of charge/discharge cycles of given Depth of Discharge (DOD). Since the lifetime of the battery also depends on the average depth of discharge during cycling (expressed in percentage (%) of rated capacity), the cycling capability may be more conveniently expressed by multiplying this average depth of discharge by the battery lifetime expressed in number of cycles. The result is called the Nominal Cycling Capability, which is expressed as the number of equivalent 100 % nominal capacity cycles. The starter battery typically has a low cycling capability of less than 100 nominal cycles, which means that it is able to withstand for example 500 cycles of maximally 20 % depth of discharge. The battery appropriate for PV application requires a good cycling capability of at least 500 nominal cycles, which means that it should be able to withstand for example 1000 cycles of 50 % depth of discharge (fig. 4).
Fig.4. Cycle life as a function of deep of discharge