[LINK] transmission losses (was Re: Past the Black Stump - Was Hot Rocks

[Greg Taylor]

On 2011/04/04 9:07 PM, Tom Koltai wrote:
>> -----Original Message-----
>> From: link-bounces at mailman.anu.edu.au
>> [mailto:link-bounces at mailman.anu.edu.au] On Behalf Of Greg Taylor
>> Sent: Monday, 4 April 2011 8:19 PM
>> To: link at mailman.anu.edu.au
>> Subject: Re: [LINK] Past the Black Stump - Was Hot Rocks
>>
>>
>> On 2011/04/04 6:10 PM, Tom Koltai wrote:
>>> .....
>>> Umm, not really. My understanding was that it was to be a 2
>> MW plant,
>>> with transmission loss on a cold day being 2kW per kilometre
>>> (conservatively) than the deliverable to 100 Km distance is
>> only 90%
>>> of generated power. @ 200 kilometres, 80% of Gen. power.
>>>
>>> For the Portland customer, they would only be able to
>> deliver -200 kW.
>>> (yep minus 200 KW) .....
>> Power loss depends on transmission voltage and transmission line
>> resistance per km.
>>
>> What figures did you use to get your 2kW per km power loss?
>>
> I can't remember Greg, apologies, it was in 2005. However, it was the
> culmination of examining data from the various participants in the
> transmission network over three years for the entire grid on the Eastern
> Seabord of Au and taking the lowest aggregate number.
> The majority of the data was from the Nemmco archives and with obvious
> differences in aerial versus submarine. We concentrated on only the
> aerial numbers as being the majority of power distribution across long
> distances in Au.
> As a sanity check I remember we cross referenced it with some data from
> France and Germany (Alsace) and discovered many parallels.
>
> TomK

A (simplistic) back of the envelope calculation:

Power loss P =  I^2 * R   (Joule Effect)
   where I = current, and R=resistance

For a 2MW plant and a transmission line voltage of 220kV, we have:
Current I = power/voltage = 2000000/220000 = 9.09A

For power loss to be 2kW over a distance of 1km, resistance would have 
to be:
R = P/(I^2) = 2000/(9.09*9.09) = 24.2 ohms per km.

That is about the resistance of 18AWG (1mm diameter) copper wire at 25C 
(1). Transmission wires are much thicker than that, and therefore of 
much lower resistance, e.g. 0 AWG copper (9.5mm diam) has a resistance 
of 0.329 ohm/km.

Your point about transmission line length being a factor with this 
technology is well taken, but your loss figure of 2kW/km seems to be 
overstated.

Greg

(1) Source:
Wire Resistance and Voltage Drop Calculator
http://www.stealth316.com/2-wire-resistance.htm