From: ce11son@yahoo.ca   
      
   On Sun, 14 Feb 2016 15:00:31 -0600, Stephen Sprunk   
    wrote:   
      
   >On 14-Feb-16 14:08, bob wrote:   
   >> Clark F Morris  wrote:   
   >>> As I understand it, the amount of AC power that can be transmitted   
   >>> at a given voltage is inversely proportional to the voltage.  Thus   
   >>> a train that could get the required power at 15 KV 16.7 Hz could   
   >>> not get it at 15 KV 50 Hz.   
   >>   
   Where frequency does still make a difference (a diminishing feature   
   for the reasons described below), are you assuming that this is not   
   taken into account when the length of section fed by a substation   
   is/was determined ?   
      
   >> I don't follow. 15 kV is the same voltage at 50 Hz as it is at 16.7   
   >> Hz or any other frequency.   
   >   
   >The voltage and current may be the same, but the power may not be.   
   >   
   >W = V * A * pf   
   >   
   >For DC, pf=1 (aka unity), and that formula reduces to W = V * A.  For   
   >AC, though, pf (and therefore power) varies inversely with frequency.   
   >   
   >Modern AC trains are _close enough_ to unity at all frequencies that we   
   >can use the DC reduction, but older AC trains weren't.  So, be careful   
   >when reading old literature in this area.  (OTOH, if you are running   
   >museum trains, be careful when reading modern literature.)   
   >   
   >>> Also I note that at least some of the multi-voltage ICE trains and   
   >>> TGVs have different power ratings depending on the power source.   
   >>   
   >> Right, but that's because the current, and hence electrical losses   
   >> are much less at 25 kV than at 15 kV.   
   >   
   >Of course; all else being equal, 25kV requires lower current than 15kV   
   >(or 11kV) to deliver the same power.   
   >   
   >> The fact that one is 50 Hz and the other is 16.7 Hz is not the issue.   
   >   
   >It's an issue iff the trains aren't near unity, i.e. all else is _not_   
   >equal in the above statement.   
   >   
   >> There are separate frequency dependent transformer related issues,   
   >> but these are not related to the voltage.   
   >   
   >Not directly, but if the higher frequency reduces power factor, you'll   
   >need more current to get the same power at the same voltage--and that   
   >means you can't reduce transformer size by as much as the frequency   
   >increase seems to indicate.   
   >   
   >S   
      
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