From: stephen@sprunk.org   
      
   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.   
   >   
   > 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   
      
   --   
   Stephen Sprunk         "God does not play dice."  --Albert Einstein   
   CCIE #3723         "God is an inveterate gambler, and He throws the   
   K5SSS        dice at every possible opportunity." --Stephen Hawking   
      
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