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kW vs kWh

kW vs kWh

Everyone needs to understand the difference between the units kilowatt (kW) and kilowatt-hour (kWh)

Kilowatt (kW) is a unit of instantaneous power that is flowing at that very second. Like how you would rate water flow at liters per minute, Kilowatt is thousands of joules per second. So when you refer to electric vehicle power, or a solar installation, the units are in kilowatts, because that is the amount of instantaneous energy they can supply.

Kilowatt-hour (kWh) comes from the amount of kilowatts used over a period of time. The literal translation is 1 kilowatt being used for 1 hour, is 1 kilowatt-hour. Kilowatt-hour is a unit if energy used over a period of time, and not the instantaneous value. So when you refer to battery storage, the units are in kilowatt-hour, because that is the amount of energy it can supply over a given amount of time.

To recap:

Solar installation of 9kW

Energy storage of 9kWh

The solar panels would generate 9kW for 1 hour to store 9kWh of energy.

T35LAX | 18 april 2019

or:
The solar panels would generate 12 HP (horse power) for 1 hour to store 9kWh of energy ;-)

andy.connor.e | 18 april 2019

Actually, i prefer 9kg (m/s)^2

SUN 2 DRV | 19 april 2019

"Kilowatt (kW) is a unit of instantaneous power that is flowing at that very second."

SB ...at that instant, or POINT in time." ...not related to a second...

prof.bhattacharjee | 19 april 2019

Everyone understands how things are prices in almost every field except energy. While electricity is sold in the unit of kWh (10 100 W lamps, an electric stove or a refrigerator consumes 1 kWh of energy in one hour), gasoline which we buy as a source of energy is sold by the gallons. But gasoline when burned produces heat, not electricity (both are energy, but electricity is more useful as you can move objects with it). So let us compare apples to apples. Suppose we buy a gallon of gasoline and convert its energy to electricity. Will it beat the current Tesla Supercharger price of 26 cents per kWh in California?

A gallon (US) of gasoline is 3.785 liter and on a typical summer day it has density of 0.727 kg/L giving it a mass of 2.752 kg (yes, in the winter, you will get more energy from 1 gallon of gas as it is more dense, about 2.5% more fuel at 10 deg-C as opposed to 27 deg-C). One kg of gasoline when burned produces 162 kWh of heat. So from one gallon we can get 445.8 kWh. Now suppose we have a generator (that converts heat to electricity) at our disposal which has an efficiency of 30% (a large power plant has much better efficiency); this means we can produce 162*0.3 = 48.6 kWh of electricity. Even with $4/gallon price of gasoline, price per kWh become 400/48.6= 8.23 cents per kWh.

SCCRENDO | 19 april 2019

Thanks for doing the calculations. Very interesting. But you are comparing apples to oranges. Fossil fuels damage the environment so you need to factor that in to the cost of fuel. You also need to factor in the cost of oil extraction and transport of fuel. I guess we also need to price in the wars that are fought over oil. Electricity costs are also going to go down in future as we develop a greater infrastructure with solar etc.

prof.bhattacharjee | 19 april 2019

I was comparing energy prices from the standpoint of a consumer, but I totally agree with you. In san diego we have the option of buying electricity that is sourced from local solar companies (the cost is about 5-10% higher). I wish that model is adopted everywhere so that consumers don't feel that the only way to go solar is to put a rooftop unit.

mbirnie51 | 21 april 2019

Lets take the environmental impact of gas/diesel stations one step further. Consider the leakage of tanks over the years and contamination of water tables. When a fossil fuel filling station is decommissioned there is soil remediation, tank disposal and more to consider. So where do these costs get figured, in the front end or later in time? Pipeline construction (distruction really) spills and explosions are a concern, such as @sccrendo offered.

Tesla2018 | 21 april 2019

I think for cars it is easier to calculate how many miles can you go on a dollar when compsring gasoline with electricity. If gas is $4 a gallon and my car gets 40 mpg, then it gets 10 miles per dollar.

If elecricity is 10 cents per KW, then I get 10 Kw for $1. If my car can go 300 miles on 75 Kw, then it goes 4 miles on 1Kw or 40 miles on 10Kw or $1.00 worth of electricity. So even if my car gets 40 mpg on gas, it gets 4 times as much distance per dollar.

Tesla2018 | 21 april 2019

Oops. it cut me off. I get 4 times more distance per dollar using electricity.

science-isbetter | 21 april 2019

@Prof.bhattacharjee

You say, "So from one gallon we can get 445.8 kWh." What's your source for that number? I really don't know if it's correct or not, but I did a quick Internet search and I find a gallon of gasoline has 33.7 kwh. So if my search is correct, your estimate is off by an order of more than an order of magnitude making the electricity at least 82 cents per kwh. I'd be happy to be corrected.

science-isbetter | 24 april 2019

Bump to see if Prof.bhattacharjee will respond. Am I wrong by a factor of 10?

It's relevant because this post is intended to help people decide if gasoline is less expensive per mile than electricity in a Tesla.

Yodrak. | 24 april 2019

"I did a quick Internet search and I find a gallon of gasoline has 33.7 kwh."

I did the same and found 33.7 on one site and 33.4 on another. Close enough compared to the self-proclaimed Prof - he's the one who is off by a factor of 10+.

SCCRENDO | 24 april 2019

Professors also make mistakes. Good professors come back and admit their mistake or show us in a logical manner why they are correct. I guess we will find out what kind of professor he is.