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I read on Wikipedia that the Oslo Metro has regenerative braking, but no batteries to store the energy. Therefore, the energy can only be utilized if there is another train "nearby" to utilize the energy.

How far is "nearby"?

Due to the bottleneck of the common tunnel, all lines have 15 minute gaps between departures. That means that there is typically several kilometers between each train, except for on the parts of the network where several lines share the same track (such as the common tunnel and some other stretches.)

  • Why can the energy not be shared across those several kilometers?

  • Is the resistance in the wires along the track making it not worth it?

  • Couldn't the energy be fed back into the grid instead?

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    \$\begingroup\$ @Revetahw Not really. Trains have very little rolling resistance and but lots of inertia, so whenever you're not feeling acceleration it's almost certain the metro is coasting. \$\endgroup\$ – Agent_L Jan 30 at 9:33
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    \$\begingroup\$ @Agent_L don't forget air resistance. Any vehicle has a top speed, which is attained only at maximum throttle, and can be maintained only at maximum throttle. In other words, acceleration falls off as velocity increases, eventually reaching zero, but power consumption does not. \$\endgroup\$ – phoog Jan 30 at 9:44
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    \$\begingroup\$ @phoog Sure, there is air resistance (in a tunnel much higher than on surface). All I'm saying that a train traveling at 50km/h may lose merely few km/h over a kilometer or two - and that's next station already. So, the train accelerates at full power until desired speed is reached, coasts for most of the distance (motors disconnected, power drawn eg. by lights) and brakes hard at the next station. Newer stock with power electronics have fine control over power, but the old ones have just few discrete settings. As few as two, 25% (motors in series) and 100%(motors parallel) is enough. \$\endgroup\$ – Agent_L Jan 30 at 10:04
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    \$\begingroup\$ @phood When it comes to full speed, trains are limited by their DC series motors. They have funny property of getting less speed (but more torque) the more they are loaded. It's all good, but eventually the speed of the motor is limited by the train resistance. How do you go faster? You shunt part of the stator, thus decrease power, but increase top speed. So, as funny as it sounds, train at full speed has less power available than when going slow. Electrics have nothing like throttle.(That's true for simple DC drives, electronically commutated AC motors are different thing entirely.) \$\endgroup\$ – Agent_L Jan 30 at 10:14
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    \$\begingroup\$ @Agent_L I don't know the operating rules in Oslo, but in NYC the throttle generally remains at maximum unless the train is braking. There's no coasting except in contexts that require reduced speed (switches, curves, downgrades, restrictive signals, etc.). So it is very common to have situations where the passengers feel no acceleration, or very little, but the throttle is at maximum. \$\endgroup\$ – phoog Jan 30 at 10:18
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Is the resistance in the wires along the track making it not worth it?

That will be one factor. The article states that each set has 12 x 140 kW motors giving a total of 1680 kW (1.68 MW) for each train set. The system is 750 V DC and, unusually, uses third-rail in some sections and overhead lines in others. At those power levels currents in the order of 2000 A will be involved so line resistance certainly becomes an issue. Line resistance may also be a factor in circuit-breaker operation and trip times and place further constraints on the maximum length of a section.

Another factor to remember is that the power stations (basically transformers / rectifiers / filters and circuit-breakers) will be spread out along the line with sectional isolators between each power station. In this case the current can't flow from one section to the next. I suspect that this is the real reason for the "nearby" constraint.

Couldn't the energy be fed back into the grid instead?

It could, but it would require inverters to convert DC to AC and these wouldn't be cheap at those power levels and the duty cycle (the amount of regeneration time involved) may not make them worthwhile.


Additional information.

Acceleration in the range 0 to 40 kilometers per hour (0 to 25 mph) is limited to 1.3 meters per second squared (4.3 ft/s2). In this phase, the fully loaded train uses 5.0 kiloampere.

So, 5000 A max current per train. I can't find any resistance tables for steel rails so I can't provide an estimate of the voltage drop per km.

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    \$\begingroup\$ According to Wikipadia it is 750 V DC. \$\endgroup\$ – UweD Jan 30 at 7:52
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    \$\begingroup\$ It is fairly strange that capacitor/battery banks at the most central subway stops are not installed. It would have a fairly high duty cycle, since the trains are often 2-3 min apart both directions in the rush hours. \$\endgroup\$ – Stian Yttervik Jan 30 at 9:31
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    \$\begingroup\$ @StianYttervik I also wouldn't mind a mains power bank in my house. The only reason I don't have one is that I don't want to pay for it. \$\endgroup\$ – Dmitry Grigoryev Jan 30 at 10:07
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    \$\begingroup\$ @StianYttervik Cheap electricity and strict safety requirements (making all public transport-related systems expensive) do their job. \$\endgroup\$ – Dmitry Grigoryev Jan 30 at 14:03
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    \$\begingroup\$ 95% of Norway's electricity generation is hydroelectric. It's so cheap that electricity usage is 3 times higher than the European average (e.g. it is cheaper to heat your house with electricity than with gas). Recycling a few MW isn't likely to be an economically sensible option. \$\endgroup\$ – alephzero Jan 30 at 16:08
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For obvious reasons, any railway network is divided into isolated sections and each of those is powered separately from the medium or high voltage grid through its own transformer, circuit breaker and switch.

Two trains within the same section can share power directly. Trains in different sections can only do so through the grid. Since the Oslo Metro uses DC and rectifiers are usually one-way, power sharing through the grid is not available and therefore limited to trains within the same section.

The image below shows a section isolator in an AC overhead line. The sections are powered by different phases of the three-phase high voltage grid for load balancing.

Phasentrenner image source

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    \$\begingroup\$ "rectifiers are usually one-way" Not just usually, always. Something that goes from DC to AC is by definition not a rectifier but an inverter. \$\endgroup\$ – Acccumulation Jan 30 at 23:28
  • \$\begingroup\$ Do you know how large these sections are? \$\endgroup\$ – Stig Hemmer Feb 1 at 9:43
  • \$\begingroup\$ Can you elaborate on the "obvious reasons"? I have some ideas, but they're not necessarily obvious to everybody. \$\endgroup\$ – pericynthion Feb 3 at 20:56
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Electric railway guy here.

Long distance propagation

I have seen 600V trolley wire dip to only 200V four miles from the substation under heavy ~300A load from a single articulated car. (4/0 wire, 107 mm2, rails as return).

Third rails are a great deal beefier, but subway trains are a great deal heavier. Typically third rail shoes are fused at 400 amps (per shoe, and not every shoe is in contact at once) with as many as 8 cars. Oslo runs big articulated cars that are electrically 3 cars.

If the regenerated electricity passes a substation, it's even more at disadvantage.

I mean the subway train could push its regenerated power any distance if it's willing or able to increase voltage without limit. Unregulated, DC motor regen can act like an old, inductive constant-current source, increasing voltage until current flows. Burning up much of it in transmission losses would be fine, it's "free energy". However it hits limits of a) onboard equipment (not least, insulation strength in motors), and b) the third rail. BART aimed to have a 1000 volt third rail, but found the worst case scenario of rain on brake dust caused spectacular flash-overs even in their temperate climate. They backed down to 900 volts but it is still troublesome. Oslo is already at 750, not much headroom.

Really, to regenerate productively, there needs to be a train nearby already pulling the voltage down and able to gobble up those amps.

Regen onto grid

This is hard, not least because a couple megawatts of power injected for a few seconds isn't all that useful to the grid.

Also, DC-AC regen itself is hard, with large silicon inverters required at every substation.

In the Golden Age, rotary converters were perfectly capable of efficient DC-AC regen (in fact, they had circuits to prevent accidental regen, e.g. a substation's local grid having a brownout, causing it to be backfed from another substation via the trolley wire). Electric railways had more of their own AC power distribution. And third rail voltage was only 600V, so more headroom. However, the cars were not capable of it: subway trains were very simple back then, with only 7-12 wires on the inter-car control lines.

Rotary converters were abolished just as soon as mercury-arc rectifiers became available, and even those were gone by the time of the first regen cars.

I don't expect any resurgence in rotary converters (more's the pity, since they are dog simple, actually correct power factor in the local grid, and may be competitive since they are simple). So it comes down to complex, large inverters. Given the limited financial gain from selling power back, only very advanced (high R&D) systems like BART are dipping their toes into grid regen from DC.

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  • \$\begingroup\$ Thanks for the answer. What does it mean to be an "electric railway guy"? \$\endgroup\$ – Revetahw Feb 1 at 19:44
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    \$\begingroup\$ Well, I have worked on trolley wire at a heritage railway, and keep up on electric railway happenings in the USA (which, given the level of activity, isn't hard) including in preservation. \$\endgroup\$ – Harper Feb 1 at 20:41
  • \$\begingroup\$ "I don't expect any resurgence in rotary converters (more's the pity..." -> given those possible advantages, would be nice to know why you don't expect any resurgence \$\endgroup\$ – hmijail Feb 3 at 5:44
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    \$\begingroup\$ @hmijail Because the craft has been lost. It's hard enough these days finding a shop who can competently rebuild a large DC motor, let alone design-build a very large lot-more-going-on-than-motor. \$\endgroup\$ – Harper Feb 3 at 6:33
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When you're braking, your primary objective is to get rid of the extra energy, so you don't really care how efficiently it will be used. Even if resistive losses are close to 100%, having regenerative brake is better than having mechanical brakes only. So it's certainly not about power line resistance, only about what the power grid can handle.

Why can the energy not be shared across those several kilometers?

In the simple case of isolated sections, it's a trade-off between the length of a line stretch where regenerative braking is possible, and the length of a line stretch affected by an electrical failure. I.e. if the whole power network could be used for regenerative braking, a single failure would also bring the whole network down.

More complex solutions are indeed possible theoretically, but not economically.

Couldn't the energy be fed back into the grid instead?

Feeding the energy in the grid with stable energy consumption will raise the voltage very quickly, and typical power plants will not be able to shape their output fast enough to compensate. If the local grid cannot handle such overvoltage spikes, there's no point in building inverters. And even if the grid can handle extra incoming energy, the solution may be not economically viable.

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  • \$\begingroup\$ " Even if resistive losses are close to 100%, having regenerative brake is better than having mechanical brakes only." From a braking perspective, yes, but from an energy utilization perspective, that is not necessarily true. \$\endgroup\$ – Acccumulation Jan 30 at 23:31
  • \$\begingroup\$ @Acccumulation Why? How can regenerative braking be worse in terms of energy utilisation? \$\endgroup\$ – Revetahw Jan 31 at 18:20
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    \$\begingroup\$ @Revetahw The original claim was that it's better, so the negation would not necessarily be that it's worse, but just that it's not better. \$\endgroup\$ – Acccumulation Jan 31 at 18:24
  • \$\begingroup\$ @Acccumulation I see. \$\endgroup\$ – Revetahw Jan 31 at 18:26

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