From: stephen@sprunk.org   
      
   On 14-Feb-16 06:49, Clark F Morris wrote:   
   > bob  wrote:   
   >> Modern European locomotives are all designed to run on the main   
   >> four systems of 25 kV 50 Hz, 15 kV 16.7 Hz, 3 kV DC and 1500 V DC.   
   >> While they sometimes have a lower power output on DC, there is no   
   >> problem with the low frequency system.   
   >   
   > As I understand it, the amount of AC power that can be transmitted   
   > at a given voltage is inversely proportional to the voltage.   
      
   ITYM "frequency".   
      
   > Thus a train that could get the required power at 15 KV 16.7 Hz   
   > could not get it at 15 KV 50 Hz.   
      
   ... unless the train is close enough to unity that frequency doesn't   
   matter, which is the case for all modern AC trains.   
      
   > Also I note that at least some of the multi-voltage ICE trains and   
   > TGVs have different power ratings depending on the power source.   
      
   Yes; if they ran at full power on low-voltage (i.e. 3kV and 1.5kV)   
   lines, the high currents would cause catastrophic failures.  Power   
   varies with (roughly the square of) speed, so this is generally   
   implemented via lower speed limits on such lines.   
      
   This is why all new high-speed lines are 2x25kV.  Upgrading 15kV   
   (Germany et al) or 12.5kV (US) lines means higher currents than is   
   desirable; if 2x25kV isn't feasible due to clearance or other issues,   
   then 2x15kV or 2x12.5kV is a relatively inexpensive compromise.   
      
   S   
      
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