The battery bank is the workhorse of any stand alone system, because it is its stable power
source. It is thus very important to understand how the battery bank will act in the PV
system. When we want to understand how a battery works we have to consider the net
effect of all the components that try to charge or discharge the battery. In Figure 20.13 (a)
the most important currents and voltages that we need for the following discussion are
depicted. In Figure 20.13 (b) the equivalent circuit and an I-V curve of an idealized battery
bank are shown, similar to what we already discussed in Section 19.3.
As we have seen in Eq. (19.25), the voltage of the battery bank V BB will differ from
V OC-BB and is also dependent on the current I BB flowing through the battery,
where R i is the internal resistance of the battery. Remember that we use the convention
that I BB is positive when the battery is charged and negative when it is discharged.
Let us now derive an expression for V BB as a function of the other PV system
parameters. We start with the power on the left-hand and right-hand sides of the MPPT,
and hence
Consequently, β = 0 means that the PV system is not active, for example at night.
In a similar manner, we look at the power on the left-hand and right-hand sides of the
inverter:
and consequently
Combining Eqs. (20.51) and (20.53), we find
Clearly, α = 0 indicates that no load is present.
Combining Eqs. (20.49) and (20.54), multiplying with R i V BB and rearranging, leads
to a quadratic equation,
with the solutions
source. It is thus very important to understand how the battery bank will act in the PV
system. When we want to understand how a battery works we have to consider the net
effect of all the components that try to charge or discharge the battery. In Figure 20.13 (a)
the most important currents and voltages that we need for the following discussion are
depicted. In Figure 20.13 (b) the equivalent circuit and an I-V curve of an idealized battery
bank are shown, similar to what we already discussed in Section 19.3.
As we have seen in Eq. (19.25), the voltage of the battery bank V BB will differ from
V OC-BB and is also dependent on the current I BB flowing through the battery,
where R i is the internal resistance of the battery. Remember that we use the convention
that I BB is positive when the battery is charged and negative when it is discharged.
Let us now derive an expression for V BB as a function of the other PV system
parameters. We start with the power on the left-hand and right-hand sides of the MPPT,
and hence
Consequently, β = 0 means that the PV system is not active, for example at night.
In a similar manner, we look at the power on the left-hand and right-hand sides of the
inverter:
and consequently
Combining Eqs. (20.51) and (20.53), we find
Clearly, α = 0 indicates that no load is present.
Combining Eqs. (20.49) and (20.54), multiplying with R i V BB and rearranging, leads
to a quadratic equation,
with the solutions