# Electric train efficiency

Every time I take a train I sort of think about this, so the electrified overhead wire (DC or AC) and the rails form a transmission line and the train is a load that moves along the transmission line.
Let's talk about the DC case as it seems more simple, so when the train is at or near a substation feeding the overhead wire the resistance is low as there is not much distance of wire but when the train is at it's furthest point from each two substations or far away doesn't the train become very inefficient?

The local DC line is 3.3Kv, I am not sure of what the overhead wire is made up (stainless steel strands with aluminum outside?) but the rails are iron and rusty and connections etc , given that current flows in a circuit and the rails form the return path of the circuit what is the approximate efficiency of the train ?
Also if the overhead line is thousands of volts (27Kv in the AC case) above ground and rails have high resistance then aren't the rails close to the train at some rather high voltage with respect to ground?

If we look at the ICE, big fast train, wiki says typically 15kV operating voltage, 8MW max power, that's "only" 500A or so, which is actually surprisingly low. And yeah the current will create a potential but given its "only" 500A or so, its probably not that much Volts. Keep in mind it doesn't take 8MW to run it at steady speed, its more for acceleration (or braking).

Re efficiency, you can count on that they thought about this a lot (hence the high voltage), I know for the ICE they do some scheduling tricks for example to reduce the load to load distance on the line, eg one train accelerates out of a station while another is slowing down into the same station, therefore the recuperated energy from train 1 is going straight into the train 2 on the next track minimizing transmission distance.

anorlunda
Staff Emeritus
There are many designs for electric trains. It is not an easy problem. Efficiency, safety, and reliability trade off with each other. Both DC and AC have been used.

Probably most confusing is that some designs are modern, while others are more than 100 years old, but still in use.

This Wikipedia article is very interesting. https://en.wikipedia.org/wiki/List_of_railway_electrification_systems

Just to show the diversity, here's an excerpt from that article.

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davenn and dlgoff
I am kind of surprised that a bunch of European countries still use the 16Hz AC, I wonder why they did not convert it to 50Hz? Wiki says because of cost. I read some of those countries still have some small dedicated power plants producing AC output at that frequency specifically for the track. Without semiconductors the only other way to do that is rotary converter ?

Anyway no matter how high the overhead voltage the return path for ordinary trains is the rails so are the rails grounded after fixed intervals to earth ground or do they carry the return current all the way to the nearest substations that feeds the overhead line?
taking the number essenmein said of 500A it makes a large difference whether those return via a low resistance path or high resistance path ?
I tried googling but can't find any numbers with regards to the resistance of rails over some distance x

From an engineering point of view electric trains seem ridiculous , thousands of Km of HV transmition to maintain , the dangers and losses in resistance .... They surely are unable to compete with diesel electric .... trains which have a diesel generator on-board and use electric transmission to feed motors driving the train ... there is also the waste heat which can be used to keep the carriages warm...

Resistance of steel is about 10 times that of copper , not too bad , those rails are pretty chunky
50 Kg / meter in mass ...so equivalent resistance to a copper cable with a mass of 5Kg/meter

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so judging by what you said the rails are actually quite good conductors and their higher resistance is balanced out by the much much larger cross section compared to any ordinary cables? Then what about the rail connections , I have seen many in my life walking next to rail and they all seem very sloppy from an electrical contact viewpoint, there is the gap for thermal expansion on each side there is a metal brackets held together by screws and what seems like an iron cable the size of a finger connecting the two rails which I assume is for the electrical connectivity and continuity ?

You also said "dangers and losses" what dangers exactly you had in mind?

PS. it would be fun to measure actual rail resistance over some fixed length but I can't imagine how could I do that without having the added resistance of very large multi-meter probe wires, another example I can think of would be applying a DC potential across selected distance and letting a fixed current to run through and then measuring the voltage drop?
I really don't plan on doing this in real life just as a curiosity

rbelli1
Gold Member
On long electrified rail lines there is a periodic break in the supply rail or overhead line. This makes it possible to feed the line from multiple places. One drawback to this approach is that if the locomotive stops in the gap it will need a friend to give it a nudge back onto power.

BoB

Henryk
Gold Member
I am kind of surprised that a bunch of European countries still use the 16Hz AC, I wonder why they did not convert it to 50Hz? Wiki says because of cost. I read some of those countries still have some small dedicated power plants producing AC output at that frequency specifically for the track. Without semiconductors the only other way to do that is rotary converter ?
I am not quite sure but it could be to minimize losses, specifically reactive losses.
You see, in typical transmission lines operating at 50 Hz, the reactive losses are 2-4 times larger than resistive losses. Lowering the frequency reduces the reactive losses.
However, up to my knowledge, most electric trains (and streetcars) operate on DC.
From an engineering point of view electric trains seem ridiculous
If is it so ridiculous, why most countries (outside North America) switched to electric trains?
Yes, there are cost associated with building a supply network. On the other hand, electricity is produced in power plants with higher efficiency and lower emission than diesel engines. Electric locomotive torque is much higher than diesel and on breaking, the kinetic energy of is fed back to the grid. Not to mention the noise. I used to live in a valley town with a rail line going up the hill. I could hear the diesel engines pulling the trains up at more than 10 miles away. Kind of annoying, especially at night when you want to get some sleep.

Dr.D
As a passenger of the train, you might use a smartphone to monitor the magnetic field produced by the current in the overhead line. The magnetic field is proportional to the current. If the B-x diagram is linear between two substations, the losses are small. If, however, there is a big dip halfway between the substations, the losses are serious.

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But that happens mostly only with third rail electrification not with the overhead wire , in my country i can't remember when was the last time someone got electrocuted because we only have overhead wires.

I think I have actually seen those points where the overhead wire splits and it is around halfway between two feeding substations, even if the train stops there its okay because the wire is split in such a way that the two wires go parallel to one another for a short distance so the pantograph is always touching one of the or both of the wires.

russ_watters
Mentor
But that happens mostly only with third rail electrification not with the overhead wire , in my country i can't remember when was the last time someone got electrocuted because we only have overhead wires.

I think I have actually seen those points where the overhead wire splits and it is around halfway between two feeding substations, even if the train stops there its okay because the wire is split in such a way that the two wires go parallel to one another for a short distance so the pantograph is always touching one of the or both of the wires.
Let me expalain what has happened here...

Several posts of misinformation were deleted and the member who posted them won't be returning to the thread. Ordinarily I'd delete the whole exchange, but since it is your thread, I'm leaving your post up and instead will respond with some better sources/statistics:

Here's a BLS study of workplace related railroad fatalities from 1993-2002:
https://www.bls.gov/opub/mlr/2007/07/art2full.pdf

The total was 1,221 deaths over 10 years. Note, that includes railroad workers and others who's workplace intersects with the railroad: primarily truck drivers. It does not include normal passengers or others who are not working at the time.

Of the 460 railroad workers killed over that span, 19 (2 per year) died of electrocution. It doesn't mention electrocutions for the other categoreis; it looks to me like there were none, as almost all were collissions (with vehicles or pedestiran workers).

Here's a Newsweek article that takes a deeper dive in to New York's metro area:
https://www.newsweek.com/train-crashes-numbers-304486
There were 58 “collision with individual” (CWI) deaths on the city's subway lines last year, according to Metropolitan Transit Authority (MTA) statistics, and five non-CWI deaths, such as dying on MTA property. Between 2011 and [2014], there were 248 subway deaths in total.
Electrocution isn't mentioned, but if we assume as an upper bound that all 5 non-collession deaths were electrocutions (they certainly weren't), that would put an upper bound of about 10% overall.

Electrocution among construction workers is a bigger problem, with several hundred deaths and sevearal thousand injuries per year:
https://www.ecmag.com/section/safety/alarming-statistics

[note: By definition, "electrocution" is death.]

And for all workers of all types in all contexts, about 411 per year:
https://www.cdc.gov/niosh/docs/98-131/pdfs/98-131.pdf

anorlunda
In other words reading your post I conclude that electrocution is not a big problem certainly not in the railroad business and even less so with rails that only have overhead wires because the only way someone can com in touch with them is if they are literally working with them but those who work know their risks and are trained to do that so it is unlikely.

Surely construction seems like a bigger cause for electrocution because I know from personal experience that many people working under small contractors or even individually don't have even the basic knowledge of physics or electricity and when water, wet cement and old sometimes damaged wires all come into contact it is a recipe for disaster. My friend once accidentally while drilling into a wall hit a live cable , luckily he had those newer drills with all plastic case if he would have had the older ones with aluminum cases he probably would be dead now.

All in all I still haven't hear any numbers with regards to my main question of how approximately efficient is a typical say 3kV line or 25Kv AC line. The efficiency will probably change with rail condition and other factors but I wonder some averages?
The trains themselves have probably reached their efficiency limit some time ago as the electric motors both DC universal ones and AC induction ones have hit their peak efficiency decades ago.

russ_watters
anorlunda
Staff Emeritus
The efficiency will probably change with rail condition and other factors

The biggest factor is distance from the source. Because they can be sourced from transmission substations, the distances vary widely, and so to the efficiencies. As a wild guess, I would say 85% on the average. If the efficiencies were much lower than that, the rails would be warm to the touch, be ice and snow free in winter, and would appear to glow in infrared images.

russ_watters
Mentor
All in all I still haven't hear any numbers with regards to my main question of how approximately efficient is a typical say 3kV line or 25Kv AC line. The efficiency will probably change with rail condition and other factors but I wonder some averages?
The trains themselves have probably reached their efficiency limit some time ago as the electric motors both DC universal ones and AC induction ones have hit their peak efficiency decades ago.
So, this is why I think the question may not be well formed: Regardless of the electrical efficiency of a power delivery system, the average total system efficiency is always zero.

So to me, the more relevant "efficiency" metric would be something like kwh per passenger or ton mile (km).

anorlunda, your reasoning sounds logical but I don't get it how in the world those rusty rail connections can have low enough resistance, on average per every 1 km there are a number of such connections, I see on high speed rails they thermite weld most connections leaving a few physical spacings for heat expansion , the welded connections probably have lower electrical resistance but for older slow speed rail I see all connections are mostly with rail spacing and brackets and screws holding the rails together with an old usually rusty metal cable connecting the two.

russ, I think humans are so lightweight compared to trains especially the older all metal ones that an average half full train makes no real difference for the power consumed while traveling, especially given that rails have very low traction/rolling resistance so unlike a car with heavier load makes the tire resistance much higher I doubt a train feels it unless we are speaking about a fully loaded freight train

One more point somehow indeed that rusty iron can have such low resistance because they also send low voltage signals down the rails which monitor train movement across the tracks as the train wheels short circuit the rails at any given point and I guess they then calculate the trains positions based on electrical resistance of the shorted signal so in order to know the train position every given distance of rail must have equal resistance , at least that's my reasoning based on what I know.

All in all I still haven't hear any numbers with regards to my main question of how approximately efficient is a typical say 3kV line or 25Kv AC line. The efficiency will probably change with rail condition and other factors but I wonder some averages?.

According to a report, 10% of the electrical energy supplied by the substation is dissipated in the resistance of the overhead lines in my area. Increasing the voltage from 1.5 kV to 3 kV would reduce the loss to 2.5%. Losses in the rails are never mentioned, apparently it is negligable. It is continuous welded rail

russ_watters
Mentor
russ, I think humans are so lightweight compared to trains especially the older all metal ones that an average half full train makes no real difference for the power consumed while traveling, especially given that rails have very low traction/rolling resistance so unlike a car with heavier load makes the tire resistance much higher I doubt a train feels it unless we are speaking about a fully loaded freight train...
I agree, but I don't think you followed my point. So I'll ask explicitly: by what quantity do you want to measure "electric train efficiency"?

And:

jim hardy
Gold Member
Dearly Missed
by what quantity do you want to measure "electric train efficiency"?
Now there's an interesting prospect.

Efficiency is ##\frac{output}{input}##
Input would be energy?
Output would be {tons X miles} or{passengers X miles} ?

Fuel Efficiency

Moving freight by rail is 4 times more fuel efficient than moving freight on the highway. Trains can move a ton of freight over 470 miles on a single gallon of fuel. Efficient use of fuel means fewer greenhouse gas emissions for our planet. (Learn more at the Association of American Railroads’ website, http://www.aar.org/.)

Here is the formula for our 201 fuel efficiency rating: (From the 2015 R-1 Report)

• Schedule 750, Lines 1+3, Diesel Fuel Consumed (freight + switching) = 487,540,790 gallons

• Schedule 755, Line 110, Revenue Ton-Miles = 229,562,353,000245,212,180,000 RTM (Revenue Ton Miles -jh)

• RTM per gallon = (229,562,353,000 RTM / 487,540,790 gals) = 471 RTM/gal

but for electrics i'm having difficulty.

An interesting paper here

compares electric and diesel on a "Well to Rail" basis by accounting for where the waste heat is produced
and converting kwh into equivalent gallons of diesel fuel..

They compare two commuter systems,one electric in SE Pennsylvania and one mostly diesel near Chicago.

and conclude the energy efficiency isn't much different at all when comparing car-miles per unit of energy

what makes the difference is how long you make the trains and how full you fill them.

same paper states
Thermal efficiency of electric locomotives, when measured from the pantograph (or power meter) to the work performed by the wheels at the rails, is approximately 76-85%.

old jim

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russ_watters
anorlunda
Staff Emeritus
compares electric and diesel on a "Well to Rail" basis by accounting for where the waste heat is produced
and converting kwh into equivalent gallons of diesel fuel..

Good stuff Jim. But here's a couple of comments
• Waste heat for the power plant depends on the type of plant, steam/hydro/solar PV all have radically different numbers.
• Note that those comparisons do not mention resistive losses in the power transmission. That suggests that those losses are negligible. This whole thread centers on the OPs estimates of resistive losses.

russ_watters
russ_watters
Mentor
• Note that those comparisons do not mention resistive losses in the power transmission. That suggests that those losses are negligible. This whole thread centers on the OPs estimates of resistive losses.
In the chart with the curved arrows, isn't that the little one just to the right of the dotted line?

anorlunda
Staff Emeritus
In the chart with the curved arrows, isn't that the little one just to the right of the dotted line?
Yes. But in the two plots of MPG versus year, there is no mention of transmission losses.

Of course actual losses depend on where the power is generated. In SE PA, some power plants are local, some power comes from Hudson's Bay in Canada. Averaged nationwide, T&D resistive losses are 5.9% (https://data.worldbank.org/indicator/EG.ELC.LOSS.ZS) But it is likely that the study Jim cited assumes locally generated power, so they didn't bother to calculate actual losses.

russ_watters
Ok when russ asked me in what way I want to measure the efficiency then since I already stated that at least for passenger train their weight load is a negligible with respect to the energy used , I basically want to measure the efficiency from an electricity input vs mechanical output standpoint.
To be more specific since part of an electric train is the track and overhead wire I want to measure from the substation feeding that wire because there is no electric train without the wire and the return path. So my efficiency would be measured from assuming that if we put 100% in the overhead wire how much of that results in pure mechanical force pushing the train forward (plus the equipment necessary for the train system to work) and how much is wasted as resistance heat over the wire and rails and also for AC systems in reactive power from inductors (motors, solenoids) etc.
I do realize this is rather complicated analysis and yes I did try to search my question and could not find any direct answer.

The reason I am not concerned with power plant efficiency is because that is another topic as they supply not just trains but cities and factories and homes, also as anorlunda said the thermal efficiency or inverter or any other efficiency depends on the plant in question.
So I measure from the feeding substation because then we can compare the efficiencies with diesel-electric for example because all of their energy is 100% in the loaded fuel tanks and all of the energy for an electric train is 100% at the output wires connected to the overhead line further from there the energy begins to drop as resistance losses etc.

Jim cited that on average the electrical efficiency of an electric train goes from 76 to 85% which sounds very plausible so assuming an 80% efficient modern electric locomotive we should then subtract from those 80% the losses in the overhead wire/third rail and also the losses in the rails themselves. Then we could come up with a number that could be said is the total electric efficiency of an electric locomotive which let's say would be 70% (just a guess).

Then we could further subtract the losses in the rail feeding substations and the wires that lead from the national grid to that substation which would further reduce the overall efficiency.
Now from a "green" perspective in terms of which mode of transport causes less CO2 it would be interesting to see specifically in terms of railroad whether electric really has lower emissions than diesel-electric (again talking specifically about railroad applications) because if we consider all the added complexity of electric trains as overhead wires, wire holding posts, substations, wires to the substations , maintenance etc I sort of feel that diesel-electric could even produce less CO2 than purely electric.

Ofcourse if all our electric power plants would be 100% CO2 free then this point would loose it's meaning but since they are not it is still a valid point.

russ_watters
Mentor
...I basically want to measure the efficiency from an electricity input vs mechanical output standpoint.
To be more specific since part of an electric train is the track and overhead wire I want to measure from the substation feeding that wire because there is no electric train without the wire and the return path. So my efficiency would be measured from assuming that if we put 100% in the overhead wire how much of that results in pure mechanical force pushing the train forward (plus the equipment necessary for the train system to work) and how much is wasted as resistance heat over the wire and rails and also for AC systems in reactive power from inductors (motors, solenoids) etc.
Jim gave a number in post #18 of about 80% from the electric meter to the wheels, which seems reasonable to me.

What concerns me is how this number is digested/what it is used for. It may give a false impression of how much improvement is available (if that's what you are after): it can imply you can only do up to 25% better. But since as I said before the total system efficiency of a transportation system is always zero, there is actually no limit to how much the energy use can be improved.

continuing from post #23 one more thing I want to add and ask at the same time, now a diesel electric locomotive has a large diesel and large modern diesels with electronic fuel systems are having efficiencies up to 30/35% now since the wiring is very short in the locomotive the resistive losses in the wires/rails/substations etc are not present so could it be that if the electricity for an electric train is produced in a power plant that uses thermodynamic cycle which has an average efficiency of 30 to 35% then the diesel electric would win out ? because thinking logically a coal plant producing steam driving a turbine which drives a generator have roughly the same energy efficiency than a large diesel running at constant rpm turning a generator the only difference being that in the diesel the electricity can be used on the spot.