# Battery Charging and Discharging Parameters

The key function of a battery in a PV system is to provide power when other generating sourced are unavailable, and hence batteries in PV systems will experience continual charging and discharging cycles. All battery parameters are affected by battery charging and recharging cycle.

### Battery State of Charge (BSOC)

A key parameter of a battery in use in a PV system is the battery state of charge (BSOC). The BSOC is defined as the fraction of the total energy or battery capacity that has been used over the total available from the battery.

Battery state of charge (BSOC or SOC) gives the ratio of the amount of energy presently stored in the battery to the nominal rated capacity. For example, for a battery at 80% SOC and with a 500 Ah capacity, the energy stored in the battery is 400 Ah. A common way to measure the BSOC is to measure the voltage of the battery and compare this to the voltage of a fully charged battery. However, as the battery voltage depends on temperature as well as the state of charge of the battery, this measurement provides only a rough idea of battery state of charge.

### Depth of Discharge

In many types of batteries, the full energy stored in the battery cannot be withdrawn (in other words, the battery cannot be fully discharged) without causing serious, and often irreparable damage to the battery. The Depth of Discharge (DOD) of a battery determines the fraction of power that can be withdrawn from the battery. For example, if the DOD of a battery is given by the manufacturer as 25%, then only 25% of the battery capacity can be used by the load.

Nearly all batteries, particularly for renewable energy applications, are rated in terms of their capacity. However, the actual energy that can be extracted from the battery is often (particularly for lead acid batteries) significantly less than the rated capacity. This occurs since, particularly for lead acid batteries, extracting the full battery capacity from the battery dramatically reduced battery lifetime. The depth of discharge (DOD) is the fraction of battery capacity that can be used from the battery and will be specified by the manufacturer. For example, a battery 500 Ah with a DOD of 20% can only provide 500Ah x .2 = 100 Ah.

### Daily Depth of Discharge

In addition to specifying the overall depth of discharge, a battery manufacturer will also typically specify a daily depth of discharge. The daily depth of discharge determined the maximum amount of energy that can be extracted from the battery in a 24 hour period. Typically in a larger scale PV system (such as that for a remote house), the battery bank is inherently sized such that the daily depth of discharge is not an additional constraint. However, in smaller systems that have a relatively few days storage, the daily depth of discharge may need to be calculated.

### Charging and Discharging Rates

A common way of specifying battery capacity is to provide the battery capacity as a function of the time in which it takes to fully discharge the battery (note that in practice the battery often cannot be fully discharged). The notation to specify battery capacity in this way is written as Cx, where x is the time in hours that it takes to discharge the battery. C10 = Z (also written as C10 = xxx) means that the battery capacity is Z when the battery is discharged in 10 hours. When the discharging rate is halved (and the time it takes to discharge the battery is doubled to 20 hours), the battery capacity rises to Y. The discharge rate when discharging the battery in 10 hours is found by dividing the capacity by the time. Therefore, C/10 is the charge rate. This may also be written as 0.1C. Consequently, a specification of C20/10 (also written as 0.1C20) is the charge rate obtained when the battery capacity (measured when the battery is discharged in 20 hours) is discharged in 10 hours. Such relatively complicated notations may result when higher or lower charging rates are used for short periods of time.

The charging rate, in Amps, is given in the amount of charge added the battery per unit time (i.e., Coulombs/sec, which is the unit of Amps). The charging/discharge rate may be specified directly by giving the current - for example, a battery may be charged/discharged at 10 A. However, it is more common to specify the charging/discharging rate by determining the amount of time it takes to fully discharge the battery. In this case, the discharge rate is given by the battery capacity (in Ah) divided by the number of hours it takes to charge/discharge the battery. For example, a battery capacity of 500 Ah that is theoretically discharged to its cut-off voltage in 20 hours will have a discharge rate of 500 Ah/20 h = 25 A. Furthermore, if the battery is a 12V battery, then the power being delivered to the load is 25A x 12 V = 300W. Note that the battery is only "theoretically" discharged to its maximum level as most practical batteries cannot be fully discharged without either damaging the battery or reducing its lifetime.

### Charging and Discharging Regimes

Each battery type has a particular set of restraints and conditions related to its charging and discharging regime, and many types of batteries require specific charging regimes or charge controllers. For example, nickel cadmium batteries should be nearly completely discharged before charging, while lead acid batteries should never be fully discharged. Furthermore, the voltage and current during the charge cycle will be different for each type of battery. Typically, a battery charger or charge controller designed for one type of battery cannot be used with another type.