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# Kilo what? kW vs kWh and other units explained

#### DITB

##### Charged.hk co-founder
Not really HK specific, but here goes:

A lot of people, even within the industry, confuse

Power ( Watt W )
Potential ( Voltage V )
Flow ( Current/ampere A)
Energy (Watt hour Wh)

As Watt is Joule per second, ( W = J/s), energy can also be expressed as J, although since Joule is pr second and Wh is pr hour, there are 3600 Joules in 1 Wh (1 Watt in for one hours is 60 seconds times 60 minutes)

Now don't leave me now, it will get more simple shortly.

Especially POWER and ENERGY are being mixed up, mainly when speaking of electric cars and solar panels, but also CURRENT vs POWER (more below). "How many kW is that solar panel?" "How many kWh is your electric car battery?". Let's get back to those in a moment.

Everyone should be very familiar with the difference between speed and distance.

Let's look at the units of those (using metrics, imperial is similar though).

Speed is km/h and distance is km. "k" is just 1000, so we could call it m/h and m, it would be all the same, or mph and miles, just different units.

The SPEED you are doing can be compared to Watt, ie what are you doing RIGHT now. How FAST are you going, what POWER is your engine using to attain this speed.

After a while - lets say one hour - you will have moved a certain DISTANCE, and used a certain amount of ENERGY.

So you maintain a certain SPEED to go a certain DISTANCE and you use a certain POWER to consume a certain amount of ENERGY.

I could rephrase that as units, saying exactly the same:

So you maintain a certain km/h (or mph) to go a certain km (or miles) and you use a certain Watt to consume a certain amount of WattHours (or Joules).

What might make it a bit confusing is that we don't use Joules pr second as we would use km/h and mph. By using Watt, we already put TIME under the fraction, making POWER expressed as "Energy consumed pr second". Hence, when we talk about SPEED, we clearly see the "pr hour" in km/h or mph, while with energy, the "pr second" is hidden inside W (which is J/s).

So from now on, when you talk about W or Wh, remember there is a hidden "divided by time" in there, which also mean that in Wh, time is removed as we multiply by hour, but divide by second. If you have used a certain amount of Wh, it doesn't really matter if it took to 5 seconds or 5 hours to use it - Wh is energy used, regardless of time.

Recap: W is the rate of energy use (power) while Wh is an amount of energy.

In your Tesla Model S, it states your Wh/km. Since Wh (or "J pr second times hour") is now divided by a distance, it is back to a "rate" again, but this time a rate pr distance, not a rate pr time as POWER is. "Joule pr second times hour divided by km" is a bit long and confusing, hence Wh/km (or Wh per mile for imperial markets).

As for the solar panel industry, the very common mistake of confusing kW and kWh often goes like this:

Solar panels (electric in this example) are rated at how much POWER they can produce by most optimum sun position with a clear blue sky. This is Wp or kWp, the peak (maximum) Watt of POWER. Over the year, a certain statistical amount of sunshine is expected, hence (depending on geographical location), the ENERGY produced by a solar PV installation in one year can be roughly estimated from the peak POWER. Typically, this could be 2/3s of the Wp times 1000, ie a 3kWp installation could yield 2000 kWh in a year. While W is measured pr second and Wh is pr hour (3600 seconds), it might not make sense but then there is thousands of hours of sunshine typically - in the end, this could amount to the "2/3" conversion, while remembering to also multiply by 1000.

What this means is that since a 1000 Wp doesn't give 1000 kWh unless you have exactly 1000 hours of 100% sunshine at an optimum angle, the "performance" of solar panels are often confused. "How many Watts is your solar power?" Some would answer correctly the Wp, ie what is the maximum POWER you can extract, while others would answer how many kWhs pr year they expect (or usually get). No, it isn't easy, and hence this is often confused!

If you have followed me so far, it brings us into the next issue with units: Voltage, Current and Power

There is a great chart here of different charging standards:

Request Rejected or All The Electric-Car Charging Connectors In One Great Big Poster

Yet even from the "ev-institute", they confuse power and current, here is an extract from the lower right hand corner of this chart: (Maybe by the time you read this post, the chart has been updated to correct "current" to "power")

Just like the rate of energy you extract from your car is expressed in W (or kW, or HP) is called POWER, so is the maximum rate of energy you get back into the battery, by charging, also POWER, not "current".

So what is the difference between current and power? And Voltage? It's all confusing, let me try to make it easy (I hope!)

This time, imagine a water tap/faucet, from here on just called tap. There is some kind of supply of water, forcing water under pressure to make it's way to your tap. We can compare this to electricity in this way:

Voltage: The pressure of the water, like "PSI" or "bar" (v for volt)
Current: The amount of water flowing (A for ampere)
Power: The pressure of the water times the flow (W for Watt - voltage times the amps, can be either Watt or Joule/second)

and let's just add for later use:

Resistance: Smaller pipes (thinner electric wire), higher resistance to flow (R or greek omega, for Ohm, electric resistance)

We all know that if you open all taps in the house, the flow of water will go down at each tap, and the pressure of the water will be less. Someone in the shower, while another member of the family turns on the hot water nearby: "Hey, who took the hot water?" as the pressure of the hot water drops, the cold/hot mixture in the shower suddenly has its balance offset making it much colder (severity depending on the plumbing)

In your garden, you want to water your plants with your garden hose, and to make the stream of water go further, you restrict the flow with your finger (or a nozzle), to make a more concentrated beam go further. The FLOW will be LESS, but the PRESSURE goes UP, hence you get a stream of water that reaches further. But with all the taps on in the house, you won't get as much of range.

If you want more water out, you need either more pressure (voltage) or wider pipes/tubes (thicker cables, more current). While your garden hose could be a electric mains wall jack, a fire hose would be a supercharger, boasting both higher pressure (powerful pump, higher voltage) and more flow (wide fire hose, thicker cable). Hence a thicker cable means more amps (current), yet current alone does not give POWER. To make charging as fast as possible, you need BOTH a higher voltage (better insulation) AND more current (thicker cable)

Mathematically, this is part of Ohms law(s), the one with

P = U x I

which is the same as Watt = Volt x Ampere

The other one states

I = V / R

which is ampere = volt divided by resistance (ohm)

The rate at which you can recharge your car battery depends on how many Watt the charger is rated at, which is Joule pr second, right? The rate of energy delivered. Hence, talking about EITHER the voltage OR the ampere for a given charger doesn't give you all the information you need - you need BOTH to know "how much you are getting".

13A charger at 220V? 2,860 Watt or 2.86 kW. Supercharger at 400V, 300A? 120,000 W or 120 kW. And so on.

As can be seen in the I = V / R, the higher the current, the more POWER (Watt) you can transfer in the same cable. This is why a 12 volt circuit like the one driving the accessories of our Model S (and most ICE cars) requires so thick cables, while 220V or even 120V appliances can use a much thinner cable to drive much more demanding utilities. To save copper (thinner wires), one can up the voltage, rather than up the amps, to get the same results - while bearing in mind that higher voltage can also jup a longer distance (requires more separation between poles). This is why long distance power transfer is done at potentials like 400,000 volt, and the cables are so far apart (higher voltage can jump further).

For most EV owners, the voltage and amps really aren't too important, if all you are concerned about is charging rates. The one single unit you are looking for is Watt (or kW). Superchargers are at a current (no pun intended) level of 110 to 120 kW, while the slowest 110V 13A charging options cannot even run the air condition of the Model S, with just 1.4 kW.

For the more technically minded - there is a little trap here as AC voltage is not a constant voltage, but varying at a certain amount of times pr second (Hz or Hertz), for instance 50Hz or 60Hz, between 0 and maximum. Hence, an AC voltage has to be divided by the square of 2 to get the "rms" voltage, or the "average voltage"

As I am no electrician and only human, I welcome the real experts to point out any errors I made in this post. Or ways to write it more clearly. As per the recently updated forum rules, you have 24 hours to guide me, after that only moderators will be able to edit this post.

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The way I explain it is:

Say you have a 1,000Watt heater. 1,000Wh (Watt Hour) is what you use when you run that heater at full blast for 1 hour. A kW is just 1,000 Watts. So, 1kWh is 1kW for 1 hour, or 1/2kW for 2 hours, or 2kW for 1/2 hour, etc.

Then, Watt is Voltage multiplied by Current. W=V x A. So, 1kW could be 4A x 250V, or 10A x 100V. The common Hong Kong 2.2kW is 10A x 220V.