7 ms·

I have a question about the power grid I've never gotten a satisfactory answer to. I hope someone here can help. If the USA's power grid is about 4,000,000 me

I have a question about the power grid I've never gotten a satisfactory answer to. I hope someone here can help. If the USA's power grid is about 4,000,000 meters wide, and the electric signal propagates at roughly the speed of light (3 x 10^8 m/s) (https://physics.stackexchange.com/questions/358894/speed-of-light-vs-speed-of-electricity https://physics.stackexchange.com/questions/358894/speed-of-...), then it will take roughly .013 seconds for the electrical signal to reach from one station to another. This is a lot out of phase! (the period of 60 Hz is .016 sec) How is this managed? If two generating stations on opposite ends of the country are both contributing to the electrical signal, how is this time lag accounted for? I have two guesses: 1. The power network is "mapped" such that there is one central generating station and all other generating stations are time lagged based on their graph distance from this generating station 2. All stations try to generate simultaneously, with their output signals interfering with eachother to a certain degree. This might not matter much because their local loads dampen the strength of their signal. Either way seems to introduce inefficiencies.

ceejayoz 9y ago
https://en.wikipedia.org/wiki/Continental_U.S._power_transmission_grid https://en.wikipedia.org/wiki/Continental_U.S._power_transmi... > The electrical grid that powers mainland North America is divided into multiple regions. The Eastern Interconnection and the Western Interconnection are the largest. Three other regions include the Texas Interconnection, the Quebec Interconnection, and the Alaska Interconnection. Each region delivers 60 Hz electrical power. The regions are not directly connected or synchronized to each other, but there are some HVDC interconnections.
maxerickson 9y ago
There's splits in the grid: https://en.wikipedia.org/wiki/Continental_U.S._power_transmission_grid https://en.wikipedia.org/wiki/Continental_U.S._power_transmi... So that takes care of some of it. Anyway, synchronization is actively managed, when a generator starts up, it is synchronized to the grid adaptively. https://en.wikipedia.org/wiki/Synchronization_(alternating_current) https://en.wikipedia.org/wiki/Synchronization_(alternating_c...
- CompelTechnic 9y ago
  Even with the splits in the grid, the time lag is still significant, I would think. The western interconnection appears to be 3,700,000 from the corner of Arizona to the corner of British Columbia. The wikipedia article doesn't address the time lag (except perhaps implicitly).
  - kortex 9y ago
    Indian Point to Yankee Nuclear is 230 km, IP to Niagara Falls is 440, and NF to YN is 500 km. At c (electronic energy propagates slighly slower), 1 km = 4.32' (arcminute) of lag. That means the 'legs' of this triangle have lag of 16, 32, and 36 degrees. That around half a Hz of frequency out of phase, or ~0.9%. By comparison, the 2011 tornado outbreak caused 0.09 Hz deviation. So there must be some accounting for this propagation error, either as losses, or engineering. What I suspect (totally not my field) is that the high power interconnects between large generators do have this triangular lag (the incoming lines lag from the plant's reference frame), but they use quadrature boosting or similar to match that particular interconnect. T&D (transmission & distribution) result in ~6% of the net energy being wasted. I imagine phase lag "feels" like impedance, with the real component acting as resistance. Also, it's worth noting part of the appeal of HVDC, aside from line reactance and skin effect, is you get to choose your output frequency. https://www.nema.org/Products/Documents/TDEnergyEff.pdf https://www.nema.org/Products/Documents/TDEnergyEff.pdf
- adamcharnock 9y ago
  Reading about this for the first time, it sounds like this problem would also apply to the Synchronous grid of Continental Europe [1] discussed in the press release. This is approx 4000km across, and much more if you include Russia (I'm not clear on the extent of the grid). It does not sound like these are split into individual grids. Maybe active synchronisation solves this, but to my (inexpert) mind the network would still suffer from interferences at various points between power plants. [1] https://en.wikipedia.org/wiki/Synchronous_grid_of_Continental_Europe https://en.wikipedia.org/wiki/Synchronous_grid_of_Continenta...
radiowave 9y ago
Stations within the same grid are in sync, plus or minus propagation delays. When a newly started up station wants to connect to the grid, it has to get its generators in sync with the rest of the grid before being switched in. (See wikipedia entry for Synchrocope.) Once the generators are switched in, they'll inherently maintain sync, as even if there's too little motive power being supplied by the station's turbines, the difference will be made up by the power grid itself, which will drive the generators round like an electric motor. (Typically this would happen for a brief period after coming online, after which the station would throttle up and start helping to push the generators round.)
- adamcharnock 9y ago
  Ah, this is very interesting. Thank you.
- hollander 9y ago
  If stations are not in sync, will that mean they cancel eachother out like with soundwaves and anti-sound?
  - radiowave 9y ago
    I imagine that they might cancel out, given limitless current flows between them. In practice, something would go bang long before that happened.
    - XorNot 9y ago
      You're missing resistance losses, essentially. They would do no work (no real power component to the load impedance mismatch) but I^2 * R means the complex component would be entirely lost to transmission lines / coil windings. But the effect is as you say: something goes bang.
  - clord 9y ago
    All the other generators in that grid will drive the out-of-sync station like an electric motor at a faster or slower speed until it's synched up. In effect that's what's happening in the article. Unaccounted load is pulling other generators down, making the frequency unexpectedly low. Perhaps they're not using just frequency to coordinate (solar/wind perhaps needs a sidechannel?), and someone on their grid in a politically unstable area is using power without reporting on the side-channel. Hence the frequency drops due to the unaccounted load.
aleh 9y ago
This propagation delay does not really matter as long as neighboring power plants are synchronized with each other. Yes, east coast and west coast are out of phase, but only to a perfect observer who can see phase value on both coasts instantly (without a propagation delay). However in reality information about the phase cannot travel faster than speed of light, so to any real observer anywhere between east and west coasts both sides appear to be in sync.
pjc50 9y ago
Synchronisation is purely local. They are, from the point of view of a sky observer, out of phase by the amount you say, but that doesn't matter. Each generator need only sync up at the time of connection. Imagine you are on half a tandem bicycle. You are in a room with the chain of the tandem vanishing beyond the wall. You can't see, but clearly someone else is pedalling the thing as the pedals are rotating. Getting on it is tricky, as you have to rotate your feet at the right speed, but once you're on you can sit there and let it carry them round - or you can start applying pressure through your feet to do work and accelerate the chain system. At this point you discover the thing on the other end of the chain is not a person but a 60Hz synchronous motor-generator. Congratulations, you are in sync with the grid and (when pushing on the pedals) contributing power. (A corollary of this is that if your grid connection is down or the grid is split into two pieces, you can't start up again until you get a grid input to know you're in phase. See "black start" for details on this.)
- gpvos 9y ago
  Okay, but what if you are at point A, and connected to points B and C, which are 1000 km away from you and also 1000 km away from each other, and connected to each other. Now if you would synchronize with B and C, then seen from the sky B and C would be in sync with each other because they're at the same distance from you. But how would B and C then transfer power over the 1000 km link between each other without phase problems?
  - TheRealPomax 9y ago
    Remember that power stations do not generate the same single phase signal that you tap into in your house. They generate three phase AC current. They also don't link up directly: there are transmission substations in between.
    - wintermutesGhst 9y ago
      This is what I wondered, is network topology carefully arranged to avoid triangular connections, or 'loops' where a generator could interfere (indirectly) with itself?
rjmunro 9y ago
As well as the other answers here, you can control flows around grids by using a special arrangement of transformer to shift the phase of the signal. See: https://en.wikipedia.org/wiki/Quadrature_booster https://en.wikipedia.org/wiki/Quadrature_booster and here is a commercial example: https://www.siemens.com/global/en/home/products/energy/high-voltage/transformers/phase-shifting-transformers.html https://www.siemens.com/global/en/home/products/energy/high-...
howard941 9y ago
Almost all of the other replies are excellent. In light of your question I think you'll find interesting this realtime map that shows how far out of whack the regional grids are from 60Hz: http://fnetpublic.utk.edu/frequencymap.html http://fnetpublic.utk.edu/frequencymap.html
- core-questions 9y ago
  Seems like there's plenty of deviation in North America, more even than the European grid is complaining about. Quebec and the Maritimes seem to oscillate between low and normal, and the west seems to always be a bit too fast.
  - howard941 9y ago
    Yeah you're seeing the short term variation at that site, and there's plenty of it. But over a 24 hour period - for now anyway - NERC standards require time error correction, http://www.nerc.com/files/BAL-004-0.pdf http://www.nerc.com/files/BAL-004-0.pdf Going forward it may not be a good idea to rely on the grid's timebase as there's talk as well as an NPRM out there to do away with the standard. https://www.federalregister.gov/documents/2010/03/29/2010-6481/time-error-correction-reliability-standard https://www.federalregister.gov/documents/2010/03/29/2010-64...
- retromario 9y ago
  That's a really cool visualization. Do you know if anything like this exists for the European grid?
  - _trampeltier 9y ago
    http://www.netzfrequenz.info http://www.netzfrequenz.info All power grids are connected, so there is just one frequency.
    - retromario 9y ago
      Aren't all the grids in US/Canada also connected? My understanding was that they are all connected and that the grandparent visualization was showing the frequency differences across major portions of the US/Canada grid. Or am I getting this wrong?
gumby 9y ago
> If the USA's power grid is about 4,000,000 meters wide BTW North America actually has eight transnational (USA/Canada) interconnection authorities or "regions" in which power distribution is managed; it's not a unitary entity.
maliker 9y ago
Yep, as others have pointed out, grid operators can see waves of frequency change propogate through the system. Here’s some visualizations of that (see the linked movies) from a cool project called FNET/GridEye: http://fnetpublic.utk.edu/sample_events.html http://fnetpublic.utk.edu/sample_events.html
neltnerb 9y ago
I love this brain teaser. If you want to make it even more weird, consider that the second plant is communicating it's phase back to the first one! Paradox! But the answer is contained in the parent comment. Each plant generates more power if the phase lags and produces less if the phase leads. Basically, electricity consumers drag on the phase and the plants use this to control output power, so that the phase matching can be done purely locally. But it is a lot simpler if you use high voltage DC! If you do that you can connect networks with entirely different phases!
amluto 9y ago
Having thought about this before, here's how I think it works. The relevant effect isn't the speed of light per se -- it's the phase velocity v of 60 Hz AC power transmission, which is indeed reasonably close to c. If you have a power line of length l running East to West and the phase on the Western end lags by 2pil/v, then an electromagnetic calculation will show that power is moving Westward [1]. If the western phase leads, then power flows Eastward. If the phase is the same everywhere, then no current or power flows. This is actually quite handy. When demand locally exceeds supply, the phase will lag (this is how generators work), and power will flow toward the excess demand. More advanced grid operators use various devices to intentionally shift the phase to control the flow of power. [2] [1] Actually calculating this is surprisingly complicated. You can integrate the Poynting vector; you can model the inductance and capacitance of the line, calculate the current, and use P=I*V; or you can probably do it in several other ways. You might even be able to model it as little packets of energy moving along at the group velocity. [2] This ability is important for economic and engineering reasons. Imagine you connect two cities with two parallel, competing transmission lines. One has 100 MVA capacity, and one has 10 MVA capacity, but they have the same impedance. (This is a bit farfetched, but capacity is related to impedance, heat dissipation ability, and the ratings of whatever equipment is at the ends of the lines.) Without some kind of active control, to much power will flow through the 10 MVA line and it will fail.

ceejayoz 9y ago

https://en.wikipedia.org/wiki/Continental_U.S._power_transmission_grid https://en.wikipedia.org/wiki/Continental_U.S._power_transmi... > The electrical grid that powers mainland North America is divided into multiple regions. The Eastern Interconnection and the Western Interconnection are the largest. Three other regions include the Texas Interconnection, the Quebec Interconnection, and the Alaska Interconnection. Each region delivers 60 Hz electrical power. The regions are not directly connected or synchronized to each other, but there are some HVDC interconnections.

maxerickson 9y ago

There's splits in the grid: https://en.wikipedia.org/wiki/Continental_U.S._power_transmission_grid https://en.wikipedia.org/wiki/Continental_U.S._power_transmi... So that takes care of some of it. Anyway, synchronization is actively managed, when a generator starts up, it is synchronized to the grid adaptively. https://en.wikipedia.org/wiki/Synchronization_(alternating_current) https://en.wikipedia.org/wiki/Synchronization_(alternating_c...

CompelTechnic 9y ago
Even with the splits in the grid, the time lag is still significant, I would think. The western interconnection appears to be 3,700,000 from the corner of Arizona to the corner of British Columbia. The wikipedia article doesn't address the time lag (except perhaps implicitly).
- kortex 9y ago
  Indian Point to Yankee Nuclear is 230 km, IP to Niagara Falls is 440, and NF to YN is 500 km. At c (electronic energy propagates slighly slower), 1 km = 4.32' (arcminute) of lag. That means the 'legs' of this triangle have lag of 16, 32, and 36 degrees. That around half a Hz of frequency out of phase, or ~0.9%. By comparison, the 2011 tornado outbreak caused 0.09 Hz deviation. So there must be some accounting for this propagation error, either as losses, or engineering. What I suspect (totally not my field) is that the high power interconnects between large generators do have this triangular lag (the incoming lines lag from the plant's reference frame), but they use quadrature boosting or similar to match that particular interconnect. T&D (transmission & distribution) result in ~6% of the net energy being wasted. I imagine phase lag "feels" like impedance, with the real component acting as resistance. Also, it's worth noting part of the appeal of HVDC, aside from line reactance and skin effect, is you get to choose your output frequency. https://www.nema.org/Products/Documents/TDEnergyEff.pdf https://www.nema.org/Products/Documents/TDEnergyEff.pdf
adamcharnock 9y ago
Reading about this for the first time, it sounds like this problem would also apply to the Synchronous grid of Continental Europe [1] discussed in the press release. This is approx 4000km across, and much more if you include Russia (I'm not clear on the extent of the grid). It does not sound like these are split into individual grids. Maybe active synchronisation solves this, but to my (inexpert) mind the network would still suffer from interferences at various points between power plants. [1] https://en.wikipedia.org/wiki/Synchronous_grid_of_Continental_Europe https://en.wikipedia.org/wiki/Synchronous_grid_of_Continenta...

radiowave 9y ago

Stations within the same grid are in sync, plus or minus propagation delays. When a newly started up station wants to connect to the grid, it has to get its generators in sync with the rest of the grid before being switched in. (See wikipedia entry for Synchrocope.) Once the generators are switched in, they'll inherently maintain sync, as even if there's too little motive power being supplied by the station's turbines, the difference will be made up by the power grid itself, which will drive the generators round like an electric motor. (Typically this would happen for a brief period after coming online, after which the station would throttle up and start helping to push the generators round.)

adamcharnock 9y ago
Ah, this is very interesting. Thank you.
hollander 9y ago
If stations are not in sync, will that mean they cancel eachother out like with soundwaves and anti-sound?
- radiowave 9y ago
  I imagine that they might cancel out, given limitless current flows between them. In practice, something would go bang long before that happened.
  - XorNot 9y ago
    You're missing resistance losses, essentially. They would do no work (no real power component to the load impedance mismatch) but I^2 * R means the complex component would be entirely lost to transmission lines / coil windings. But the effect is as you say: something goes bang.
- clord 9y ago
  All the other generators in that grid will drive the out-of-sync station like an electric motor at a faster or slower speed until it's synched up. In effect that's what's happening in the article. Unaccounted load is pulling other generators down, making the frequency unexpectedly low. Perhaps they're not using just frequency to coordinate (solar/wind perhaps needs a sidechannel?), and someone on their grid in a politically unstable area is using power without reporting on the side-channel. Hence the frequency drops due to the unaccounted load.

aleh 9y ago

This propagation delay does not really matter as long as neighboring power plants are synchronized with each other. Yes, east coast and west coast are out of phase, but only to a perfect observer who can see phase value on both coasts instantly (without a propagation delay). However in reality information about the phase cannot travel faster than speed of light, so to any real observer anywhere between east and west coasts both sides appear to be in sync.

pjc50 9y ago

Synchronisation is purely local. They are, from the point of view of a sky observer, out of phase by the amount you say, but that doesn't matter. Each generator need only sync up at the time of connection. Imagine you are on half a tandem bicycle. You are in a room with the chain of the tandem vanishing beyond the wall. You can't see, but clearly someone else is pedalling the thing as the pedals are rotating. Getting on it is tricky, as you have to rotate your feet at the right speed, but once you're on you can sit there and let it carry them round - or you can start applying pressure through your feet to do work and accelerate the chain system. At this point you discover the thing on the other end of the chain is not a person but a 60Hz synchronous motor-generator. Congratulations, you are in sync with the grid and (when pushing on the pedals) contributing power. (A corollary of this is that if your grid connection is down or the grid is split into two pieces, you can't start up again until you get a grid input to know you're in phase. See "black start" for details on this.)

gpvos 9y ago
Okay, but what if you are at point A, and connected to points B and C, which are 1000 km away from you and also 1000 km away from each other, and connected to each other. Now if you would synchronize with B and C, then seen from the sky B and C would be in sync with each other because they're at the same distance from you. But how would B and C then transfer power over the 1000 km link between each other without phase problems?
- TheRealPomax 9y ago
  Remember that power stations do not generate the same single phase signal that you tap into in your house. They generate three phase AC current. They also don't link up directly: there are transmission substations in between.
  - wintermutesGhst 9y ago
    This is what I wondered, is network topology carefully arranged to avoid triangular connections, or 'loops' where a generator could interfere (indirectly) with itself?

rjmunro 9y ago

As well as the other answers here, you can control flows around grids by using a special arrangement of transformer to shift the phase of the signal. See: https://en.wikipedia.org/wiki/Quadrature_booster https://en.wikipedia.org/wiki/Quadrature_booster and here is a commercial example: https://www.siemens.com/global/en/home/products/energy/high-voltage/transformers/phase-shifting-transformers.html https://www.siemens.com/global/en/home/products/energy/high-...

howard941 9y ago

Almost all of the other replies are excellent. In light of your question I think you'll find interesting this realtime map that shows how far out of whack the regional grids are from 60Hz: http://fnetpublic.utk.edu/frequencymap.html http://fnetpublic.utk.edu/frequencymap.html

core-questions 9y ago
Seems like there's plenty of deviation in North America, more even than the European grid is complaining about. Quebec and the Maritimes seem to oscillate between low and normal, and the west seems to always be a bit too fast.
- howard941 9y ago
  Yeah you're seeing the short term variation at that site, and there's plenty of it. But over a 24 hour period - for now anyway - NERC standards require time error correction, http://www.nerc.com/files/BAL-004-0.pdf http://www.nerc.com/files/BAL-004-0.pdf Going forward it may not be a good idea to rely on the grid's timebase as there's talk as well as an NPRM out there to do away with the standard. https://www.federalregister.gov/documents/2010/03/29/2010-6481/time-error-correction-reliability-standard https://www.federalregister.gov/documents/2010/03/29/2010-64...
retromario 9y ago
That's a really cool visualization. Do you know if anything like this exists for the European grid?
- _trampeltier 9y ago
  http://www.netzfrequenz.info http://www.netzfrequenz.info All power grids are connected, so there is just one frequency.
  - retromario 9y ago
    Aren't all the grids in US/Canada also connected? My understanding was that they are all connected and that the grandparent visualization was showing the frequency differences across major portions of the US/Canada grid. Or am I getting this wrong?

gumby 9y ago

> If the USA's power grid is about 4,000,000 meters wide BTW North America actually has eight transnational (USA/Canada) interconnection authorities or "regions" in which power distribution is managed; it's not a unitary entity.

maliker 9y ago

Yep, as others have pointed out, grid operators can see waves of frequency change propogate through the system. Here’s some visualizations of that (see the linked movies) from a cool project called FNET/GridEye: http://fnetpublic.utk.edu/sample_events.html http://fnetpublic.utk.edu/sample_events.html

neltnerb 9y ago

I love this brain teaser. If you want to make it even more weird, consider that the second plant is communicating it's phase back to the first one! Paradox! But the answer is contained in the parent comment. Each plant generates more power if the phase lags and produces less if the phase leads. Basically, electricity consumers drag on the phase and the plants use this to control output power, so that the phase matching can be done purely locally. But it is a lot simpler if you use high voltage DC! If you do that you can connect networks with entirely different phases!

amluto 9y ago

Having thought about this before, here's how I think it works. The relevant effect isn't the speed of light per se -- it's the phase velocity v of 60 Hz AC power transmission, which is indeed reasonably close to c. If you have a power line of length l running East to West and the phase on the Western end lags by 2pil/v, then an electromagnetic calculation will show that power is moving Westward [1]. If the western phase leads, then power flows Eastward. If the phase is the same everywhere, then no current or power flows. This is actually quite handy. When demand locally exceeds supply, the phase will lag (this is how generators work), and power will flow toward the excess demand. More advanced grid operators use various devices to intentionally shift the phase to control the flow of power. [2] [1] Actually calculating this is surprisingly complicated. You can integrate the Poynting vector; you can model the inductance and capacitance of the line, calculate the current, and use P=I*V; or you can probably do it in several other ways. You might even be able to model it as little packets of energy moving along at the group velocity. [2] This ability is important for economic and engineering reasons. Imagine you connect two cities with two parallel, competing transmission lines. One has 100 MVA capacity, and one has 10 MVA capacity, but they have the same impedance. (This is a bit farfetched, but capacity is related to impedance, heat dissipation ability, and the ratings of whatever equipment is at the ends of the lines.) Without some kind of active control, to much power will flow through the 10 MVA line and it will fail.