From: stephen@sprunk.org   
      
   On 15-Feb-16 03:42, rcp27g@gmail.com wrote:   
   > 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.   
      
   I've never found a detailed description of how the relation works, but   
   here it's sufficient to say that when frequency goes up, power factor   
   goes down, and since voltage is fixed in this application, that means   
   either power goes down or current goes up.   
      
   In the instant case, while power factor _does_ go down, it is still so   
   close to unity that the difference is immaterial, so we can keep using   
   the DC reduction.   
      
   >> 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.   
      
   Clark's comments stem from a presentation several decades ago, when   
   power factors were much lower, which led the speaker to a different   
   conclusion then than the same analysis would today.   
      
   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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