Differences between the Milwaukee Road's two electrified divisions - Trains Magazine

Dan, Rails West,

The question is far from stupid, the answer does involve a bit of very basic electrical engineering, math and details of the installation, specifically sizes of contact wire, feeders and rail.

The "as-built" description of the electrification can be found in CERA bulletin 116 on "page 34" (page number in quotes as that was from the original article and not for the book). The spacing between the Doris and Kittitas  substations was 23.0 miles, the spacing between the Taunton and Doris Substations was 34.9 miles. Contact wire for almost all of the Milwaukee electrification was a pair of 4/0 copper wires (211Mcm, where Mcm means 1,000 circular mils). Feeders on the system was typically a single 500Mcm copper cable, however the stretch between Doris and Kittitas was equipped with a pair of 700Mcm copper cables, and a pair of 500Mcm cables from Doris to the bottom of the grade, which 5.3 miles away. The line was equipped with 90 lb rail.

The limitations on how far a substation can provide power is defined by how much current can be consumed and how much voltage drop is tolerable. Voltage drop is simply current times resistance for DC wiring. A simple rule of thumb is that the resistance of 1 foot of 1 cmil wire (i.e. a round wire with a diameter of 0.001", which is 1 mil) is 10.6 ohms, thus 1000' feet of 1000Mcm cable will have a resistance of 0.0106 ohms. The resistance of rail is about the same as a copper conductor with an area of 10Mcm per pound per yard, a pair of 90 lb rails is equivalent to a 1,800Mcm copper cable.

For the stretch between Doris and Kittitas, the resistance of the overhead works out to 0.7 ohms, and the resistance of the return rails also work out to be 0.7 ohms, for a total resistance of 1.4 ohms. Assuming you're willing to tolerate a 1,000V drop, this would allow Kittitas to feed 1000/1.4=714 amps to a train at Doris (or vice versa), which is substantially less than the 2,000 amps that Doris could provide as built (3,000 amps after 1955). Halfway between Doris and Kittitas, the total resistance to each substation is 0.7 ohms, or equivalent parallel resistance of 0.35 ohms. With a 1000V allowable drop, the train could pull 1000/0.35=2850 amps, 2000 amps could be supplied with a 700V drop. More sharing could occur if the size of the feeder was increased, circa 1950 aluminum cable would get you one third the resistance for a given price than copper cable - going to 3,600Mcm copper equivalent for the positive feeder and 1,800Mcm copper equivalent for the negative feeder would double the amount of power that could be shared or double the distance between substations.

As for the "reach of a substation", the answer depends on the voltage regulation strategies used by the substations as well as substation spacing and feeder size. If the substations try for constant voltage in normal operation, then a train will be drawing power from both of the nearest substations, with more power drawn from the closer substation (and no power from more distant substations). If the substations use a drooping voltage to limit current draw, then the "reach" of the substation can exceed the substation spacing, however the distant stations will be providing minimal power.

As for more than one train taking power from a substation: The dispatcher and the engineers do need to take substations limits into account when dispatching or running trains. A busy line will typically have substations at closer intervals than a line with light traffic and those substations may have higher individual capacity. The designers of the San Diego trolley's Mission Valley line overlooked this issue - a major stop on the line is Qualcom stadium and they had problems with inadequate substation power in dealing with the end of game rush.

Hope this clears things up more than it confuses...

- Erik