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Photograph of transformers installed in transmission lines.
Power is distributed over large distances at high voltage to reduce power loss in the transmission lines. The voltages generated at the power plant are stepped up by passive devices called transformers (see Transformers ) to 330,000 volts (or more in some places worldwide). At the point of use, the transformers reduce the voltage transmitted for safe residential and commercial use. (Credit: GeorgHH, Wikimedia Commons)

Power losses are less for high-voltage transmission

(a) What current is needed to transmit 100 MW of power at 200 kV? (b) What is the power dissipated by the transmission lines if they have a resistance of 1 . 00 Ω size 12{1 "." "00" %OMEGA } {} ? (c) What percentage of the power is lost in the transmission lines?

Strategy

We are given P ave = 100 MW size 12{P rSub { size 8{"ave"} } ="100"`"MW"} {} , V rms = 200 kV size 12{V rSub { size 8{"rms"} } ="200"`"kV"} {} , and the resistance of the lines is R = 1 . 00 Ω size 12{R=1 "." "00"` %OMEGA } {} . Using these givens, we can find the current flowing (from P = IV size 12{P = ital "IV"} {} ) and then the power dissipated in the lines ( P = I 2 R size 12{P = I rSup { size 8{2} } R} {} ), and we take the ratio to the total power transmitted.

Solution

To find the current, we rearrange the relationship P ave = I rms V rms size 12{P rSub { size 8{"ave"} } = I rSub { size 8{"rms"} } V rSub { size 8{"rms"} } } {} and substitute known values. This gives

I rms = P ave V rms = 100 × 10 6 W 200 × 10 3 V = 500 A . size 12{I rSub { size 8{"rms"} } = { {P rSub { size 8{"ave"} } } over {V rSub { size 8{"rms"} } } } = { {"100 " times " 10" rSup { size 8{6} } " W"} over {"200 " times " 10" rSup { size 8{3} } " V"} } =" 500 A"} {}

Solution

Knowing the current and given the resistance of the lines, the power dissipated in them is found from P ave = I rms 2 R size 12{P rSub { size 8{"ave"} } = I rSub { size 8{"rms"} } rSup { size 8{2} } R} {} . Substituting the known values gives

P ave = I rms 2 R = ( 500 A ) 2 ( 1 . 00 Ω ) = 250 kW . size 12{P rSub { size 8{"ave"} } = I rSub { size 8{"rms"} } rSup { size 8{2} } R = \( "500 A" \) rSup { size 8{2} } \( 1 "." "00 " %OMEGA \) =" 250 kW"} {}

Solution

The percent loss is the ratio of this lost power to the total or input power, multiplied by 100:

% loss= 250 kW 100 MW × 100 = 0 . 250 % . size 12{%" loss=" { {"250"" kW"} over {"100"" MW"} } ´"100"=0 "." "250 %"} {}

Discussion

One-fourth of a percent is an acceptable loss. Note that if 100 MW of power had been transmitted at 25 kV, then a current of 4000 A would have been needed. This would result in a power loss in the lines of 16.0 MW, or 16.0% rather than 0.250%. The lower the voltage, the more current is needed, and the greater the power loss in the fixed-resistance transmission lines. Of course, lower-resistance lines can be built, but this requires larger and more expensive wires. If superconducting lines could be economically produced, there would be no loss in the transmission lines at all. But, as we shall see in a later chapter, there is a limit to current in superconductors, too. In short, high voltages are more economical for transmitting power, and AC voltage is much easier to raise and lower, so that AC is used in most large-scale power distribution systems.

It is widely recognized that high voltages pose greater hazards than low voltages. But, in fact, some high voltages, such as those associated with common static electricity, can be harmless. So it is not voltage alone that determines a hazard. It is not so widely recognized that AC shocks are often more harmful than similar DC shocks. Thomas Edison thought that AC shocks were more harmful and set up a DC power-distribution system in New York City in the late 1800s. There were bitter fights, in particular between Edison and George Westinghouse and Nikola Tesla, who were advocating the use of AC in early power-distribution systems. AC has prevailed largely due to transformers and lower power losses with high-voltage transmission.

Questions & Answers

anyone know any internet site where one can find nanotechnology papers?
Damian Reply
research.net
kanaga
Introduction about quantum dots in nanotechnology
Praveena Reply
what does nano mean?
Anassong Reply
nano basically means 10^(-9). nanometer is a unit to measure length.
Bharti
do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
Damian Reply
absolutely yes
Daniel
how to know photocatalytic properties of tio2 nanoparticles...what to do now
Akash Reply
it is a goid question and i want to know the answer as well
Maciej
characteristics of micro business
Abigail
for teaching engĺish at school how nano technology help us
Anassong
Do somebody tell me a best nano engineering book for beginners?
s. Reply
there is no specific books for beginners but there is book called principle of nanotechnology
NANO
what is fullerene does it is used to make bukky balls
Devang Reply
are you nano engineer ?
s.
fullerene is a bucky ball aka Carbon 60 molecule. It was name by the architect Fuller. He design the geodesic dome. it resembles a soccer ball.
Tarell
what is the actual application of fullerenes nowadays?
Damian
That is a great question Damian. best way to answer that question is to Google it. there are hundreds of applications for buck minister fullerenes, from medical to aerospace. you can also find plenty of research papers that will give you great detail on the potential applications of fullerenes.
Tarell
what is the Synthesis, properties,and applications of carbon nano chemistry
Abhijith Reply
Mostly, they use nano carbon for electronics and for materials to be strengthened.
Virgil
is Bucky paper clear?
CYNTHIA
carbon nanotubes has various application in fuel cells membrane, current research on cancer drug,and in electronics MEMS and NEMS etc
NANO
so some one know about replacing silicon atom with phosphorous in semiconductors device?
s. Reply
Yeah, it is a pain to say the least. You basically have to heat the substarte up to around 1000 degrees celcius then pass phosphene gas over top of it, which is explosive and toxic by the way, under very low pressure.
Harper
Do you know which machine is used to that process?
s.
how to fabricate graphene ink ?
SUYASH Reply
for screen printed electrodes ?
SUYASH
What is lattice structure?
s. Reply
of graphene you mean?
Ebrahim
or in general
Ebrahim
in general
s.
Graphene has a hexagonal structure
tahir
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Cied
what is biological synthesis of nanoparticles
Sanket Reply
what's the easiest and fastest way to the synthesize AgNP?
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China
Cied
types of nano material
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I start with an easy one. carbon nanotubes woven into a long filament like a string
Porter
many many of nanotubes
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Yasmin
what is the function of carbon nanotubes?
Cesar
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Uday
what is nanomaterials​ and their applications of sensors.
Ramkumar Reply
how did you get the value of 2000N.What calculations are needed to arrive at it
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Source:  OpenStax, College physics ii. OpenStax CNX. Nov 29, 2012 Download for free at http://legacy.cnx.org/content/col11458/1.2
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