6

In a large distribution grid, it is said that consumers and producers must be in balance; what that means physically, in correct (not simplistic) mathematical formulation, is not clear: perfect balance doesn't exist in nature and I'm fighting to understand how the out of balance system either stores and retrieves energy, and at what time scale the balancing done.

What are the short term energy flows?

When I turn on a light switch, power flows in the instant. Where is it taken from?

How much energy is present in the distribution network itself at any given time? Does it fluctuate?

Is there a good yet accessible description of the elasticity of the power system? Does it vibrate?

curiousguy
  • 531
  • 1
  • 4
  • 6
  • 1
    TL/DR : the supply frequency is a good indicator of the state of balance. In the UK right now it's 50.035 Hz, so lightly loaded (more supply than demand) –  Oct 26 '19 at 22:32
  • 1
    Where does it go? Who stores it? – curiousguy Oct 26 '19 at 22:39
  • 1
    @curiousguy No one stores it, outside of comparatively tiny amounts stored in the capacitance and inductance of transmission lines and larger amounts stored in the rotational kinetic energy of turbines. Edit: Well, there are also the batteries used with PV arrays, I guess, and electric vehicles. – Hearth Oct 26 '19 at 22:51
  • @Hearth I mean in a pure simple grid w/ no fancy electric stuff, e-devices, smart-something-something... just a few industrial motors, lifts, and lights. Go back to the 50ties grid if you want. If perfect balance is not accomplished, it implies net energy level changes. Like an out of balance filling up emptying bathtub. – curiousguy Oct 26 '19 at 22:59
  • Nobody stores it : the frequency is slightly high and so is the voltage. (Or low, at other nimes) It's monitored, and generating capacity is added or removed to keep the drift within close limits. –  Oct 26 '19 at 23:20
  • @BrianDrummond Is "generating capacity" the same as produced energy? – curiousguy Oct 27 '19 at 00:29
  • @curiousguy almost but not exactly - in the short run there's a difference between *instantaneous* produced electricity (how much the generator is converting from mechanical energy to electric power at this very moment) and the generating capacity in the sense of how much extractable power is being produced by whatever is driving the turbine (steam, water, etc); a turbine might produce slightly less or more electricity than capacity temporarily as it speeds up/slows down; but changing generating capacity requires changes to the physical process that drives the turbine or adding new generators. – Peteris Oct 27 '19 at 22:48
  • @Peteris So the fast balancing is obtained by the difference between electric power and heat/pressure power? – curiousguy Oct 28 '19 at 00:18
  • If we're talking about 10 second response, then I'd say that yes, for normal operation that (steam pressure in thermal or nuclear, water kinetic energy in a hydro plant) would be the "reservoir of power" from which the balance would be maintained, in addition to pure mechanical rotational inertia - in the case of *major* mismatches we'd see some other balance mechanisms triggered such as disconnecting parts of the grid; and for "fast balancing" on the scale of 5 minutes or on the scale of milliseconds again different physical aspects would dominate. – Peteris Oct 28 '19 at 00:43

3 Answers3

11

Grid frequency is where the magic hides....

There is energy storage in the inertia of all that spinning steel, and more the other side of those throttle valves in the PE of hot water trying to be steam.

The grid frequency is really the integral of the difference between generation and load divided by the total mass moment of inertia in the system.

$$\omega=\int{(Generation - Demand) dt}/k$$

You set the base load generators to go to full output if the frequency drops below say 50.5Hz, the mid cost stuff to go throttle up at 50Hz and the peaking plants (Expensive to run) to load up if the frequency drops below say 49.8Hz (There are way more graduations then this).

The effect is that the base load runs at full power, the mid cost stuff tracks the demand and the peaking plants idle until the mid cost stuff fails to meet demand at which point they load up.

Reactive power flow controls the system voltage and by controlling this you can control the load currents in the transmission network.

The dynamics are actually quite interesting especially during fault conditions and there are whole books written on that subject.

Dan Mills
  • 17,266
  • 1
  • 20
  • 38
  • 1
    With varying production of wind turbines and varying and not completely randomized user demand, this sounds like a deck of cards in the wind. Do home building items help the controlling loop? Like lifts, toasters, iPhone chargers? – curiousguy Oct 27 '19 at 00:32
  • I wouldn't focus too much on frequency - the net would also be stable if it were a pure DC net. It just boils down to the simple P=U²/R and R>0 in this case. – asdfex Oct 27 '19 at 09:49
  • 2
    DC works for point to point links, and is in fact (when they get big enough) sometimes the optimum choice, but it gets horrifically complicated when dealing with large numbers of generators in a geographically dispersed grid. Quite apart from the obvious problems with stepping DC up and down, and the difficulty with circuit protection on high voltage, heavy current DC lines, grid control is a headache. In an AC network, frequency is sufficient to control generator output and reactive power controls network voltage. – Dan Mills Oct 27 '19 at 11:26
  • 2
    On the other hand, the stabilization scheme using frequency also only works because of large synchronous motors and generators - it would break down if only frequency-insensitive loads were present, e.g. like stepping power supplies or asynchronous motors. – asdfex Oct 27 '19 at 12:18
  • @asdfex Are you sure, I don't think the nature of the load much matters. Sure synchronous machines add inertia to the whole scheme, which is helpful, but the lions share of the inertia is probably on the generation side. Reactive power is in any case easy to control. The trap is that you do need the inertia from somewhere, and inverters are not good at providing it (Or the large amount of reactive power sometimes needed to clear a fault). You could almost see the solar plants adding big synchronous capacitors to add the ability to clear faults. – Dan Mills Oct 27 '19 at 12:47
  • 1
    Local appliances have little impact and get smeared into the noise. Load creeps up and down gradually, but when there is a load dump (say a large factory has emergency off). you can introduce hiccups that can cause desynchronization. I think a missing point is the frequency synchronizes all producers and consumers together. Without this you don't have a grid. A single user like a large train or factory should be easily accomodated by all the inertia in the grid in time to stay synchronized. When the approximation of "infinite producer" goes away such a load dump can take the grid offline – crasic Oct 27 '19 at 16:44
  • @curiousguy no, with the exception of a few "smart thermostats" that participate in load shedding programs, and maybe some big industrial users that have special agreements, the loads don't participate in balancing. And no, it's not that huge a problem. The system is big, the law of large numbers is on our side, and the network and the generation plant are *engineered* by people who have data and, more often than not, some idea of what they're doing. – hobbs Oct 27 '19 at 21:15
  • 1
    @hobbs the users don't have to do anything to participate in the balancing - any AC motor that's driven directly by grid frequency (which includes most simple motors, both small and huge) inevitably participates in the balancing as they consume slightly less power if the frequency is lower; and much less power during rapid decrease in frequency, and vice versa for frequency increases. That's how it works for thousands of people vacuuming their homes, that's how it works for a factory driving a conveyer belt. However, such motors are becoming a smaller and smaller part of the total grid load. – Peteris Oct 27 '19 at 22:55
  • @Peteris Is that true for a vacuum cleaner with a movable button to adjust power? – curiousguy Oct 28 '19 at 00:23
  • Is this balancing analogous to an inverted pendulum, where consumers add disturbances and producers quickly compensate? I could imagine that working if the inertia of the system is large compared to the control period. – user1202136 Sep 27 '21 at 21:22
5

The grid can be imagined - and in some cases is - a single generator. The generator has a speed governor to maintain the frequency. The governor will have a certain reaction time and that means that should the load suddenly increase that the frequency will drop and if the load suddenly decreases the frequency will suddenly rise.

enter image description here

Figure 1. A mechanical governor. The vertical shaft is driven by the engine and the faster it goes the more the weights are thrown outward and upward (against gravity) causing the lever arm to reduce throttle. Source: Centrifugal governor.

I worked on one of these on a 1 MVA generator and, with the aid of a reed frequency meter was able to set the frequency of the generator very close to 50 Hz.

In a large distribution grid, it is said that consumers and producers must be in balance;

Correct. In your basic grid network there is no storage. The generators can only export if there is a load. The generators may be spinning and producing voltage but if there is no load then no current will flow. The energy source (steam, diesel, hydro, etc.) will have to be reduced quickly to prevent the frequency increasing.

perfect balance doesn't exist in nature

Yes it does. The floor beneath me is providing an upthrust which exactly matches the force of gravity on my body.

... and I'm fighting to understand how the out of balance system either stores and retrieves energy, ...

It doesn't.

... and at what time scale the balancing done.

That depends on the physical governor.

What are the short term energy flows?

Energy flow is determined by the load.

When I turn on a light switch, power flows in the instant. Where is it taken from?

From the generator via the grid.

How much energy is present in the distribution network itself at any given time? Does it fluctuate?

Is there a good yet accessible description of the elasticity of the power system? Does it vibrate?

Transistor
  • 168,990
  • 12
  • 186
  • 385
  • "_The energy source (steam, diesel, hydro, etc.) will have to be reduced quickly_" And if they don't, where is that excess energy "lost"? Or balancing works in that case? "_perfect balance doesn't exist in nature_" "_Yes it does._" This is were I'm lost. Does the floor know how much support you need? What about train passing on a bridge? "_From the generator via the grid._" Then other users should be robbed of power, no? – curiousguy Oct 27 '19 at 00:26
  • The EPRI [Power System Dynamics Tutorial](https://www.epri.com/#/pages/product/1016042/?lang=en-US) is a really good read that should help you. It is free for download. – relayman357 Oct 27 '19 at 01:40
  • In case of an enormous step change in load that cannot be accommodated by speed governors in time , all producers may desynchronize and effectively take the grid down cascading to more and more plants. . At which point you will need to shut down and start everything again. – crasic Oct 27 '19 at 16:42
  • 1
    In other words, taking your train example. The grid frequency will droop by an imperceptible amount as the train energizes. as the size of the load increases or the generating power decreases such that the load is a relatively large portion of generating capacity this frequency change may be a step function. At which point the grid must adjust in the manner described by this and other answers, and if this does not happen, desynchronization will occur. – crasic Oct 27 '19 at 16:53
1

How does it store energy at electrical speeds?

It doesn't need to store an energy reserve if it can shed load. Power is energy/time. So if it can reduce power, that is as good. Fortunately, power is voltage x current. In a nominally constant-voltage system, the customer largely decides current, but the supplier decides voltage.

It can shed load by reducing voltage.

If voltage sags, generators are able to make proportionately more current, which is what the customer is really drawing. Many customer loads, however, are resistive, or at least, linear.

So this provides an insta-shed mechanism.

It can shed capacity by increasing voltage

Reverse of above. But it is also pushing power farther and fartyer out across the grid, and that consumes power two ways: transmission losses and phase disagreement with faraway generators. Because of the speed of light.

Consider two cities 600km apart on the same grid, thqt's 2 milliseconds at the speed of light. That is 36 or 45 degrees on the AC sinewave. So if power abruptly changes direction due to load changes, that is going to cause a lot of wire heating.

Harper - Reinstate Monica
  • 21,639
  • 27
  • 68
  • If the "beat" moves from producers to consumers, how can you even have multiple producers? – curiousguy Oct 27 '19 at 21:57
  • 1
    @curiousguy they all synchronize to each other. Once there are enough producers the wave is fairly stable for normal operation and self syncs. The interesting case is how you start this thing to begin with, generally a few high power plants that synchronize the next tier and so on. I am sure there are side channel synchronization of grid scale for subsets of stations or entire grid segments. Additionally, when enough production is lost and large load fluctuations may occur (national emergency event) it can take the whole thing offline through desynchronization grid-wide – crasic Oct 28 '19 at 01:48
  • @crasic I made that a separate full blown Q: [What is the speed of “electricity”?](https://electronics.stackexchange.com/q/464689/205979) – curiousguy Oct 28 '19 at 01:49