kW Versus kWh

One of the most misquoted terms in the solar industry is referencing kW when referring to kWh or vice versa. In most cases the context it is used in helps the listener to work out what is being said but in order to set the record straight let us define it properly, and simply.

In general, when talking about an inverter or a charger, you would normally be talking about its power capability. Power is measured in watts.

1000W equals a kilowatt or kW for short. A 5kW inverter would be able to supply 5kW of power at any given moment.

Let’s say you connect a 4.5kW geyser to your inverter. You would be able to cater for this load because your inverter has sufficient power for the load that is connected. If you added another 4.5kW geyser, the total load will be 9kW and your 5kW inverter does not have the power rating to supply it and it will trip on overload.

Now comes the question, how long can I power this geyser for? This is where kilowatt hour (kWh) comes in. Kilowatt hour is a measure of energy. And will give you a clue on how long you can supply a load, at a certain power output.  Let us say you have a 5kWh battery. The term 5kWh does not specify how much power can be drawn at a particular moment. For example, a 5kWh lead acid battery can easily supply 12kW! This is seen in the UPS industry where batteries are sized to last 15min or less, under huge discharge currents.

When you are talking about batteries, the first thing you want to know is “how long will they last” and it can be helpful to talk about kWh of the battery, instead of the ampere-hours or Ah rating.

Ampere-hour or Ah is also a measure of stored energy, but is not immediately helpful because the appliances we want to connect are normally rated in watts. Ah is a different unit of measurement, so we must convert it to kWh.

To get an approximate value, the simplest way is to use the nominal voltage of one battery “block” and multiply it by the Ah rating. Then multiply that number by the total number of blocks in the system.

For example, if you have 4 x 12V batteries in series to make 48V, and they are 200Ah (@ 10 hour discharge rate) each:

12V x 200Ah x 4 = 9600 Wh. (1 string x 4 series)

The same applies if you have a 24V system made up of 4 x 12V 200Ah. 2 blocks in series, with another two in parallel:

12V x 200Ah x 4 = 9600 Wh (2 string x 2 series)

As can be seen, when talking energy, it doesn’t matter if the DC voltage is 24V or 48V, if you have the same amount of 200Ah batteries, the energy capacity will be the same.

To work out the energy requirement for a load, you multiply the power it needs by the number of hours you want it to work.

So if it takes 3 hours for your geyser to heat up water, you need 3hours x 4.5kW = 13.5kWh.

This energy has to get from the batteries, to the geyser, and there are cables and inverters along the way, which means there are energy losses along the way. Your batteries will have to be oversized somewhat (for example 20%), to cater for these losses.

(For our avid readers, at this point it would be beneficial to study up Peukerts law – in a nutshell, if you have 100Ah battery and drain it at 100A, it will not last an hour as one might expect, but perhaps only half an hour!)

The second thing you need to know is, how much power can the batteries supply continuously.

This comes down to how many amperes the battery needs to supply and one can get an estimated value of what this should be, if you take the power in watts and divide it by the DC voltage of the total battery pack.

Let’s say a 48V system:

4500W ÷ 48V = 93.75A

It can be seen that a 24V system would require twice the current: 4500 ÷ 24V = 187.5A

If you look at the datasheet for a good 200Ah battery you will see it can deliver 400A for 10min, or even 2000A for 5 seconds!

Lithium based batteries have a BMS, whose task it is to protect the battery pack from extreme situations in either current or voltage. In order to get the long life that Lithium claim to give, the charge and discharge currents are typically limited to 0.5C. Shorter durations of higher power are sometimes allowed.

The “C” rating of a battery is a term that uses the capacity of the battery to rate its discharge ability, and further complicates the issue between kW and kWh.

It means the following: If a battery pack has a capacity of 4.8kWh, and has a power rating of 0.5C continuous it means it can supply 2.4kW continuously. (0.5 x 4.8kWh = 2.4kW) The confusion should come in because we have multiplied a dimensionless constant C, by a term that has the units “kWh” and thus the answer should still be in kWh, but alas it just magically becomes kW. (C should have the unit h^-1 to be correct but I guess its implied)

If a 4.8kWh battery is rated at 1C then it can supply 4.8kW.

The same principle applies to using Ah. Where a 0.5C rated battery of 100Ah will be able to supply 50A.

The power handling ability of lithium batteries thus needs to be considered when sizing it for a system. If we are talking about a 9.6kWh Lithium pack, it can usually delivery 4.8kW comfortably, and perhaps 9.6kW for shorter durations, whereas a fairly standard lead acid battery system at 48V,200Ah can happily dish out 19.2kW until its flat!

The normal range of Lithium Iron Phosphate batteries are rated at 1C discharge with custom options available.