Discharge capacity + charge enery losses + discharge energy losses = charge capacity.

Dear Mohamad Amin Saadati,

Battery capacity is normally given in Ah (Amp-hours) at a certain discharge current (A). The higher the discharge current, the quicker the discharge and the lower the overall capacity (Ah).

Big Discharge Current = High Discharge Rate = Lower Overall Capacity

So for example, a lead acid battery might have a capacity of 600Ah at a discharge current of 6A.

With a higher discharge current, of say 40A, the capacity might fall to 400Ah.  In other words, by increasing the discharge current by a factor of about 7, the overall capacity of the battery has fallen by 33%.

Electricity usage is billed in kWh. 1 kWh is the the electricity consumed by running a continuous load of 1000W for one hour.

The output of a solar system is also measured in kWh.

It is therefore helpful to know the capacity of a battery in kWh. This is worked out as follows:

Capacity in kWh = (Capacity in Ah x Operating Voltage (V)) / 1000

So if a battery has a nominal capacity of 500Ah and a nominal voltage of 12V, the overall nominal capacity in kWh is 500 * 12 = 6000Wh, or 6kWh.

Remember the battery only has this capacity when operating at the nominal discharge current …

Power (W): The power output of the battery in Watts is given by Discharge current (A)* Voltage (V).

So if our 500Ah battery has an operating current of 20A and an operating voltage of 12V, then it has a power rating of 240W.

When sizing the system it is important to look at the likely power input (i.e. the excess solar power) and the required output of the battery, as well as the capacity of the battery in kWh.

The C-rate (hours): Sometimes the battery specification may refer to the C-Rate or charge time (hours). The Nominal Capacity of the battery is given at this C Rate.

The discharge current can then be worked out from the C Rate and the Nominal Capacity.

For example:

If a battery has a C1 capacity of 400Ah, this means that when the battery is discharged in 1 hour, it has a capacity of 400Ah.  The discharge current would have to be 400A to discharge the battery in an hour.

If the battery has a C20 capacity of 600Ah, it means that when the battery is discharged in 20 hours, it has a capacity of 600Ah. The discharge current would have to be 30A to discharge the battery in 20 hours (600Ah / 20h).

To work out the discharge time (the “C Rate”) from the Nominal Capacity and the Discharge current, divide the Nominal Capacity by the Discharge Current.  This will give you the C Rate.  So if the Nominal Capacity is given as 400Ah at a discharge current of 25A, this equates to a C Rate of 16 hours (400Ah divided by 25A). In other words all parameters are relevant to a charge cycle of 16 hours. They should not be assumed to hold with a charge and discharge cycle of 4 hours.

When comparing different batteries, it is important to compare the Nominal Capacity of each battery at the same-C Rate – in other words compare the performance of the batteries over a similar charge / discharge time period.

It is also important to look at the performance of the battery over the time period relevant to the application. For most solar applications, 8 hours is a relevant charge / discharge time period.  So look at the Nominal Capacity at the C8 rate.  This will give you the discharge current required to discharge the battery over 8 hours.  From this current and the operating voltage you can work out the continuous power output of the battery over 8 hours.

Depth of discharge %: The Depth of Discharge (DoD) refers to how much energy is cycled into and out of the battery on a given cycle, expressed as a percentage of the total capacity of the battery.

Although this varies cycle to cycle, the maximum depth of discharge for lead acid batteries is typically at or below 50%. The cycle life of lead acid batteries is highly dependent on the State of Charge (SoC) that the battery is cycled at. Cycling that is done between 100% SoC and 50% SoC will last longer than the same depth of discharge cycling that is done between 70% SoC and 20% SoC. This is due to the crystalline structure changes that occur at the various states of charge.

In order to avoid the need to discharge lead acid batteries below 50% SoC, the nominal capacity of the batteries must be increased.  It is important to distinguish between the nominal capacity of the battery and the usable capacity of the battery, expressed as nominal capacity * maximum Depth of Discharge. Typically for lead acid batteries, the usable capacity = 50% of the nominal capacity.

Aqueous hybrid batteries can be cycled between any state of charge and to any depth of discharge without large impacts on the cycle life.  This reduces the need to over-size the system, it also adds flexibility to system operation. As you can see in the Aquion battery Specification Sheet above, the Depth of Discharge is given as 100%.

Lithium ion batteries can typically be discharged up to 80% before reaching a potentially harmful state of “deep discharge”.  They have a battery management system to prevent deep discharge (and over-charge).

Usable capacity and life cycles: By programming the system to limit the Depth of Discharge, the effective usable capacity of the system is limited.

Usable Capacity (Ah) = Depth of Discharge % * Nominal Capacity (Ah)

In general this will increase the number of available life cycles of the battery – the lower the programmed depth of discharge, the longer the battery will last.

System efficiency %: All batteries incur losses in the cycle of charge, storage and discharge. The round trip efficiency of the combined charger and battery is usually in the order of 83%.

Self-discharge %: Batteries gradually lose charge over time. A typical lead acid battery will lose around 5% charge a month. Self-discharge rates are lower for lithium ion batteries, although the battery safety and control circuits incorporated into lithium ion battery banks do contribute to the standing losses.

I hope I have answered your question.

With Best Wishes,

Samir G. Pandya

Dear Mohamad,

The difference between the charge and discharge capacity (Qch – Qd = Qirr) are due to the binding of lithium ions into some products taking no part in the further electrodes discharge processes: solid electrolyte interface (SEI) and cathode electrolyte interface (CEI) formations, irreversible capture in the electrode materials surface and bulk is also possible, moreover some lithium irreversible can be captured on the surface of Cu foil (as a result of CuO/Cu2O electroreduction with formation of lithium oxides and accommodation of some lithium ions on the grain boundaries structure).

Best regards,

Dr. Sergii

As Sergii Kuksenko. Also, we can find three major classes (or qualitative level staging) in Qirr related syndromes, complex processes, according to the cycling rates in Q'irr (percentage capacity loss), SOH, or SOC, and safety specs' levels.

Initial few cycles (Class1), about 1 to, about, 5 cycles, concern (capacity loss) processes due to traces of humidity and others, tiny (adsorbed, etc.) oxygen , etc. on all material inside the cell (substrates, separator, etc.).

Next cycles (Class2, Q'irr~10% to 80%SOC, about), 10 to, about, 1000 cycles, concern Qirr (capacity loss) processes due to interfaces' (SEI, CEI) and materials' surfaces aging (binder, active material grains, etc.).

Next cycles (Class3, Q'irr>80%SOC, about), 1000 to the Nc_max, concern (high Qirr capacity loss) processes due to the severe accelerated degradation of (nearly) all the materials (separator, binders and active material grains' pulverization, etc.), setting the beginning of a critical Nc period(s) and SOH phase towards cell's replacement phase, e.g. a critical service request flag for a fast replacement, in order to meet high(er) safety standard for the end-users.