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Re: power-grid physics



Hi --

Here is a snapshot of my current understanding.
This corrects some things I said earlier. Also,
it repeats some things other folks have contributed,
but I thought it would be worthwhile to have a
summary all in one place.

My primary reference is the NERC Operating Manual
(16 July 2003).
ftp://www.nerc.com/pub/sys/all_updl/oc/opman/opman.pdf.

To make sense of that document, one needs to know
some jargon and some background concepts:
-- What nerc calls an "Interconnect" is basically
what civilians would call a grid. It does not mean
an interconnection point.

-- Various pieces of the system operate as islands.
Everything within a given island is synchronous,
i.e operating at the same frequency, but different
islands are free to have different frequencies.
Indeed frequency mismatch can be used to map out
the boundaries of islands.

Normal operation is the limiting case of three huge
islands (east, west, and Texas). (The pros don't
like to apply the word island to these huge areas,
but the logic is the same.) In emergencies, the
system is supposed to break up into much smaller
islands, to prevent problems from spreading. Last
week, not nearly enough islanding occurred.

There are tie-lines between east, west, and Texas,
but they are all asynchronous DC links.

-- What nerc calls a "Control Area" is something
that has power-generation capability, a connection
to the grid, and the proper servo performance to
play by the rules described below. The smallest
possible Control Area is a single generator (with
servos) so for simplicity I will discuss that, but
in general a Control Area typically has multiple
generators and other complexities.

=====================

There are at least five different objectives that
are dealt with in four different ways. There are
nontrivial interactions between them, but let's
start by considering them separately:

1) Short-term load balancing: Suppose you have
two horses harnessed to the same wagon. You want
them to share the load. There is enough stiffness
in the harness so that if one horse tries to get
ahead of the other, it will take more than its
share of the load. The horse will feel this
instantly and will be retarded by the extra load.

The rotational version of this is
http://www.av8n.com/physics/img48/load-sharing.png

There are three disks rotating coaxially CCW. The
two outer disks (yellow) are generators. The
middle disk (green) is the load. If the turbine
driving the left-hand generator is a little
friskier than the turbine driving the right-hand
generator, the left one will become slightly
advanced in phase and will take more of the load.
Power is transferred to the load by rubber bands
shown in red. You can see that the rubber band
attached to the left disk is more stretched AND
has better leverage than the other one.

So this short-term load balancing is achieved by
basic physics. No signalling network is required;
the power lines themselves carry all the information
that is needed. No governors or servos are involved.
No software, no nuthin, just physics.

2) Phase locking: The same mechanism ensures that
the two generators will remain synchronous. The
phase signal that tells one or the other to pick
up the slack involves a *bounded* amount of phase,
so the long-term frequency is exactly the same for
both generators.

This is in some sense related to item (1), but it
is not a trivial corollary. It didn't have to be
that way. You could imagine other load-balancing
schemes, such as two generators each coupled to the
common load by a fluid clutch, so that they would
share the load but not be synchronous.

Also, if the load mismatch becomes extreme, one
generator could slip 2pi of phase relative to the
other. This would be a Bad Thing for a number of
reasons. But it drives home the point that phase
locking shouldn't be taken for granted.

3) Load regulation: Suppose that the magnitude
of the load increases.

If we had a DC system, it's clear how this would
be handled: The increased load would cause the
voltage to drop. An op-amp would notice this,
and would inform the generators to increase their
output. This is easy to arrange, by increasing
the excitation in the field coils.

You might imagine that the AC system works the
same way, but it doesn't.

They've got it rigged up so that when the load
increases, it causes both generators to slow
down. This is not just a phase shift with a
bounded amount of phase as mentioned in item (1)
and item (2), but a full-blown frequency change
involving an unbounded amount of phase.

This frequency change is detected (typically
using the finest technology from the year 1788,
namely a flyball governor) and that leads to
the opening of the throttle on the turbine
driving the generator, so that power production
comes into equilibrium with the increased load.

Now here comes a slightly sneaky bit: they
could use a PID (proportional/integral/differential)
controller on each throttle to drive the
frequency error right to zero, but they don't!
They use the system-wide (specifically, island-wide)
frequency error as a signal to all producers
to increase their power output by a certain
percentage of their capacity. This is called
frequency droop. There is a system-wide agreement
as to how each producer should respond to a given
amount of droop. Without such an agreement,
whoever had the least-droopy generator would wind
up picking up all the variations in load for the
entire island.

Again, this functionality might be seen as
piggy-backing on the phase sensitivity discussed
in item (1) and item (2), but it's not a trivial
corollary. It didn't have to be that way. It
depends on additional functionality in the
throttle servos, and on agreed-upon semantics.

Also note that they could perfectly well have
used non-droopy servos and devised some nice
out-of-band signalling scheme to do the load
regulation.

4) Long-term load balancing: The folks who own
the generators can look at the volts and amps
(or, analogously, the stretch and angle of the
rubber bands in my diagram) and see how much
power each one is generating. Then, depending
on who wants to buy and who wants to sell, they
can increase or decrease the throttle settings
on the turbines that drive the generators.
This happens on a muuuuch slower timescale than
the load-balancing mentioned in item (1) and the
load-regulation mentioned in item (3).

5) Clock synch: They count cycles. Every so
often they compare this to official time signals,
originally the Naval Observatory but nowadays
just GPS. When the discrepancy starts getting
too big, due mainly to the droop mentioned in
item (3), somebody sends out an AGC (automatic
generator control) signal that tells everybody
to bias their throttles a little bit to make
up for lost time. There are also manual procedures
for doing this. In any case, this happens on
a muuuch slower timescale than the load-balancing
and load-regulation.

The clock error can be as much as ten seconds
either way before they necessarily do anything
about it. However, the long-term frequency and
timekeeping should be excellent The phase error
is bounded, so the frequency error goes to zero
if you wait long enough. Unless there is a
blackout :-(.

6) There's all sorts of additional complexity
that comes into play when one or more generators
(or the island as a whole) reaches a limiting
case (e.g. full throttle or thermal limits) in
which case the foregoing load-balancing and
load-regulation schemes don't suffice. This
will not be explored here.

======================

Note that item (1) and item (5) can be considered
a phaselock loop within a phaselock loop. Eeeck.

BTW, if you want to learn about phaselock loops,
the beloved standard is
Floyd M. Gardner, _Phaselock Techniques_