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David Winter asked:

> With 3rd rail systems, what is the spacing between substation (ie range of
> one substation).
> 
> This will vary with system and load.
> 
> My question is looking at 3 min frequency, 6-car full size single deck
> trains, with a 750v nominal supply with either medium (+/- 100v) or wide
> tolerance (+/- 200v).
> 
> I know there's some well versed electrical engineering types who lurk
> hereabouts - so some indicative figures would be helpful noting that each
> situation requires its own assessment.
> 
> Also, what's the range of nominal voltages used with guarded types of side
> contact 3rd rail systems (eg Docklands). I know that 1200v DC was used near
> Manchester - has any system been implemented with higher DC or AC voltages
> in a 3rd rail supply?
> 
Well David, there are many more variables that require assessment to
answer your question with certainty, these include:

The traction characteristics of the train(s) involved
The stopping pattern
Geographical and topological data including gradients, curvature,
tunnels etc.
Signalling system used
The conductivity of the conductor and running rails

and so on...........

In trying to answer your question, I will assume that:

a) It is a metro type system with a maximum speed of 100km/h
b) Accelleration rate of train is 0.8m/s/s Service braking rate is
also 0.8m/s/s
c) Weight of train is 200 tonnes tare, max line current is 3000A@750V
d.c
d) Station spacing is 3000m
e) No significant civil engineering features such as severe gradients,
curves or operation within tunnels
f) Regen braking is not used
g) Conventional 3 aspect signalling is used
h) Trains use three phase drive with broadly constant power
characteristic
i) Auxiliary load is 240kW per 6 car train
j) Running rails are UIC60, grade 600 (non hardened rails) =
35milliohms per km
k) Conductor rail is 74kg/m grade 600, = 27 milliohms per km.

So, let's work this through on a very rough basis:

Train accellerates at 0.8m/s/s (average) and thus takes 34 seconds to
reach 27.7m/s (100km/h). During this time, the train will draw 3000A
continuously.At 750V, this equates to 2.25MW. Drawing from my file of
traction characteristics, a very similar train to this then requires
0.9MW to balance the losses travelling at 27.7ms speed. This equates
to 1200A at 750V.  Likewise, the train's service braking rate is the
same and will take 34 seconds to decellerate to a stand at the next
station.

Ignoring the integration required to cater for the accelleration and
decelleration phases of the journey, and using approximation, the
journey time from station to station will take about 140 seconds of
which 106 seconds will be under power (34 at 3000A and 72 at 1200A).

Let's face it, no railway ever runs properly all of the time (least of
which the one I work for) and the electrification engineer would
design this metro type system to cater for trains operating one after
the other at the signal spacing, which I am assuming will be 1000m (3
block sections between stations).

So, with the railway operating for a period with trains backed up at
every signal, between two stations, we could have 2 trains
accellerating at their maximum rate for short periods, before they
have to brake for the next signal. This could lead to a peak current
of 6000A per road.

Again, drawing from my files, whilst it is allowable under Euronorm
standards to allow for the line voltage to drop to 450V d.c from the
nominal 750V, most current designs of train would suffer from losing
time and possibly some auxiliaries such as air conditioning, if they
didn't receive 550V, so we will use that as the lowest allowable
limit.

For each km of running and conductor rail, and assuming all 4 running
rails are bonded together in parallel, the loop resistance is
35.75milliohms.

Thus for a permissible voltage drop of 200V, at 6000A, the maximum
single end feeding resistance would be 33.3 milliohms (200/6000) or
about 930m. DC electrification systems feed from both ends, so this
distance would be doubled to 1860m. If a track parallelling hut were
introduced at the electrical mid point (it has the effect of
parallelling the positive feeds and thus reducing their apparent
resistance looking from the train), this could be stretched to 2200m.
Further allowances based on diversity, driving technique and also the
engineers asking the commercial people whether they really require
full train performance when the trains are approaching red signals
would all affect the spacing considerations.

So, the strictly correct answer to your question, based on the
gargantuan assumptions I state is 1860m. However, real life ain't like
that and other considerations such as differing train types, wear
allowances, availability of land for substations, allowable
performance under perturbed conditions, driving techniques, junctions,
permissive signalling and so on and so on, would affect the spacing
decisions. When the spacings get long, a trade off needs to be made
between the size and ratings of the equipment in the substations and
their spacing (.e. few large substations versus lots of small ones),
to get an economic solution.

No voltage above 1200V d.c. has been used for conductor rail
installations on any large scale within Europe. DB has an extensive
network of such lines around Hamburg and BR used to have this system
for Manchester to Bury. This voltage is no longer standard within
Europe. All 1200V d.c systems use insulated shrouds around the rail
and either side or bottom contact.

750V d.c. systems in the UK are not insulated with the exception of
the Docklands system.

Hope this answers your question.

Richard Catlow