On Sunday, 14 February 2016 22:00:32 UTC+1, 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.   
   > >    
   > > 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.   
      
   While the frequency plays a part in the power factor, it is not as simple as   
   an inverse relationship with frequency.  It depends on whether the reactive   
   power is inductive or capacitive in nature as well as the particular   
   construction of the transformer    
   core used.   
      
   > 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.)   
      
   Right, but we aren't talking about trains from the 1950s, the trains in   
   question (Acela express and comparable) are modern, with power electronics and   
   high power factors.   
      
   > >> 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.   
      
   Right, but as you've already noted, modern trains with modern power   
   electronics, which is the case with all generations of ICE as well as Acela   
   Express are near unity power factor, so this isn't an issue.   
      
   > > 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.   
      
   Unless we're dealing with modern trains with modern power electronics and high   
   power factors, which is the case here.   
      
   Robin   
      
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