It was a thought experiment. It's clearly *possible* for many more than
the average number of stoves to be on, but as this number increases the
probability of it happening gets vanishingly small - too small to worry
If you want to be more precise, what really matters is the amount of
momentary extra load the system can tolerate (which in turn is a
function of the duration of the overload) and how often the randomness
of the load will cause it to exceed that overload threshold.
For example, if it turns out that increasing the load due to ovens from
100 MW to 150 MW for (say) 10 seconds is enough to take down part of
the distribution system by blowing a fuse or tripping a breaker, and
that event is likely to happen once a year on average, that's a
problem. If this event is likely once every thousand years, you can
Repeat this calculation for different load levels and durations. If
all possible random variation in oven load have virtually no effect on
grid reliability, then it can be ignored.
It's been a very long time since I did any statistics with real numbers,
but here's how I think you might work this out. Any given oven has a
probability p=1/3 of being on at any given time. Checking many ovens at
the same time gives a result with a binomial distribution. With a large
number of ovens, the binomial distribution approaches a normal
distribution with a mean of n*p = 33,333 and a variance of n*p*(1-p)
= 22,222 and standard deviation of 149.
This distribution has a very steep narrow peak around the mean of
33,333. 68% of the time, the actual load will be within one standard
deviation of the mean, i.e. between 33,184 and 33,482 - a change in load
of less than half a percent. 95% of the time, the load will be within
two standard deviations of mean, less than a 1% change. And it will be
within three standard deviations, still only +- 1.3 percent load change,
99.7 percent of the time.
If we only care about unusually high load, not unusually low load, we
look at the one-sided cumulative distribution. The load will exceed
33,333 ovens 50% of the time, as you'd expect. The load will go above
101% of mean (i.e. a 1% increase, to 33,667 ovens) only 1.3 percent of
the time. The load will be above 102% of mean (>= 34000 ovens on) only
4 parts per million of operating time, or about 2 minutes per year if
the ovens were left turned on 24 hours/day.
An increase of 3% above mean can be expected only 1 part per 100 billion
of time - essentially it will never happen. At 4% increase above mean
load, Excel becomes unable to calculate the probability at all.
In other words, with 100,000 of anything participating, variations of
more than a couple of percent from mean are extremely unlikely.
Thanks for volunteering to be my "human shield" on this one; maybe I
can use this time to lick a few of these self-inflicted wounds. ;-)
I suspect Dave's right. As you move into these very large numbers,
these loads, on a system-wide basis, tend to "self-balance" (no doubt
someone could quickly develop a computer model to confirm this). I'm
now thinking their greatest impact may be in terms of the local
distribution system, especially in predominately residential
neighbourhoods, as their relative size and random behaviour would hold
proportionately greater weight.
BTW, I picked 100,000 as our working number because NSP serves about
420,000 residential customers in this province and when you add in the
contributions of the smaller municipal utilities, that final tally
might reach upwards of 450,000 households; thus, we're expecting one
out of every four and a half households to be operating their ovens
during the suppertime peak and that estimate is likely to be a bit on
the high side, even though we Nova Scotians are your stereotypical
And, hey, don't forget. I owe you one!
On Tue, 13 Feb 2007 12:55:47 -0600, Mark Lloyd
On Tue, 13 Feb 2007 20:14:02 GMT, Paul M. Eldridge
Just how are these stoves interacting with each other? Something can't
happen unless there is actually some way for it to happen.
When a stove is turned on, in generates a force which is distributed
on the power line. This force is known as AWASAF (Area-Wide Anti-Stove
Activation Force). The force generated by one stove is so small that
it can be detected only with sophisticated instruments, but it is
cumulative. So much so that if 35,000 stoves are on, there is so much
AWASAF present that there is only a 1% probability that anyone can
turn on another stove. This means that the chance of 100,000 stoves
being on at once is infinitesimal.
Suppose you *did* have an oven with electronic variable power control,
where temperature controlled the "on" time of a triac. This oven would
still operate at full current until it came up to operating temperature,
and then sit at 33% duty cycle after that. The only difference between
this and what you have now is that the on/off cycle repeats every 1/120
second, rather than every couple of minutes. But that makes no real
difference to the utility, which is looking at the load averaged over
In fact, the electronic control wastes a bit of power in the switching
element, and consumes slightly *more* power than the non-electronic
oven. The triac control also distorts the utility waveform into
something that is less of a sine wave, which the utility also will not
like (the power factor gets worse, so they need higher current capacity
for the same billable watts).
Right - whether or not they have electronic controls.
Again, true with or without electronic controls.
If, however, each of these
This makes no sense. The 33% duty cycle has already been factored into
the drop from 300 MW to 100 MW. You can't divide by 3 *again*. You
need that 100 MW to keep all of the ovens at operating temperature.
This is all based on the assumption that you can somehow run all these
ovens with electronic controls on 1/3 the average power you would need
with conventional switching controls. That's nonsense - they need just
as much energy, on average, to heat the same contents to the same
temperature for the same time.
The only time it makes sense to use dimmer-like electronic power control
is when the temperature swings with conventional controls are too large.
You're right. Clearly I was a couple neurons short in my thinking.
Let me see if I can move closer to the mark this time or, failing
that, embarrass myself further trying, as the case may be.
Our basic assumption is that these elements will operate 33 per cent
of the time, once the oven reaches its set temperature. But this
cycling will be random in nature, so our 100,000 ovens won't be
cycling "perfectly" in the sense that only one-third will be energized
at any one time. As the total number of ovens increase, I take it
we'll move ever closer to this ideal scenario, but it's probably fair
to say their combined load will fluctuate due to the unevenness in
this cycling. If we were to take a series of snap shots, we might
find that perhaps 50 per cent of these elements are energized, in
which case our load at that particular moment in time is closer to 150
MW and not the 100 MW I had stated.
The point of this exercise was to determine if it might be possible to
"smooth out" or flatten this load, so its net contribution to peak can
be lowered. If we have 100,000 ovens running at a constant 1 KW each
once they reach their set temperature, their combined load should
remain fairly close to 100 MW (slightly more to account for the higher
demand during start-up). Again, my thinking is that energy
consumption should remain constant (or perhaps slightly more due to
control related losses, as you suggest), but peak demand should be
Your concerns related to power quality are well taken. There may be
ways to address that but I'm afraid I'm not very knowledgeable in this
Please let me know if I'm a little more successful this time out, or
if I should be hiding my face. :-0
How exactly is peak demand reduced? Are you using flags to signal
the neighbor not to start dinner, while you're starting yours? Or
are we doing it by ripping out the X Kwatt element and putting in one
that is 30% smaller, so we can wait longer for the oven to heat up?
Do they teach any basic science or probability where you live? Or
are you just stupid?
See my other recent post in this thread. You underestimate how strongly
large numbers of things tend to produce results that cluster around the
mean. According to my calculations, with 100,000 ovens, the likelihood
of even a 2% increase in instantaneous load due to random fluctuation is
a few parts per million. A 50% change in load is unimaginably
The triac, by switching on part way through each half-cycle of line
voltage, severely distorts the voltage and current waveform to the load
in the process of doing its job. In addition, you now have a load that
is drawing current only for the later portion of each half-cycle, and
that distorts the waveform of the *current* drawn by your house, at the
connection from the pole.
If you're dimming one 100 W bulb, this doesn't matter much, but a triac
dimmer feeding a 3 kW range element is more significant. If you had any
substantial fraction of 100,000 ovens using triac power control, the
current waveform distortion might be visible all the way back at the
generator. With *all* ovens operating this way, you're talking about
100 MW of load (on each of 3 phases) turning on part way through each
half-cycle of AC.
Also, when the current waveform departs from a sine wave and becomes
more pulse-like, resistive losses increase for the same average current.
A thought experiment to show this: suppose you draw 1 W from a DC
source by drawing 1 A at 1 V continuously. Now change to drawing 2 A
50% of the time and nothing the rest of the time. The average current
is still 1 A, and the power is still 1 W. But the resistive losses in
the wiring are proportional to current *squared*. When the switch is
turned on and you're drawing 2 A, the losses are 4 times as large as
when you were drawing 1 A. You're only drawing current half the time,
so the losses the other half are now zero, so the average loss is twice
what it was before. And that means you need twice as large a wire for
the *same* voltage drop at the same power and the same average current.
Now, you don't care about this effect. Your wiring is sized to carry
the current when the load is fully on. When you turn down the dimmer,
the total power drops and the total losses are reduced. And your meter
only bills you for the actual watts used - even though the current
waveform is distorted.
But the utility cares. It sizes its generators and lines and
transformers for the *average* load plus a safety factor, not the peak
possible load. It depends on 2/3 of the ovens being off at any given
time due to thermostat cycling. As long as any given oven or range
element is either on or off, the voltage and current waveforms at the
generator remain nice sine waves. But if all those ovens switched to
using triac controls, the current to the ovens would be zero for the
first half+ of the half-cycle, and *three times higher than average*
for the last half- of each half-cycle of the AC waveform. That requires
heavier conductors and larger transformers to deliver the same average
power to the load with the same transmission losses. It costs the
utility more to deliver the same amount of billable power, so they're
not going to be happy.
This is similar to the effect of power factor in motors. Most motors
draw current that is somewhat out of phase with the voltage. Because of
this, the power consumed by the motor is somewhat less than the volts
applied times the amps consumed. Said another way, the motor current is
*higher* than what you'd expect from the motor power and efficiency.
But the size of transformers and lines feeding a factory depends on the
amps and volts needed, not the watts. So utilities bill large factories
by the volts times amps they use, *not* watts. And factories try to
keep their power factor as close to 1 as possible.
Actually, there were electric cooktops that did this--sorta- the old
GE's with the 7 button pushbutton switches. They used coils that were
actually 2 separate coils of different wattages in one., and also had a
neutral to the switch. Highest setting was 240 to both segments of the
coil, then 240 to one and 115 the other, then 240 to one only ( and am
not sure about the exact sequence) it would put the 2 circuits in series
with 240 volts, etc, and finally on the lowest would put 115 to both in
series. In the early 70's we worked on a few ranges, and I remember the
service manager explaining this setup. I do remember going out on one
where the lady said that on certain settings none of the burners would
work right. She also said "the same time the trouble started, I found
this in the drawer underneath the cooktop", and handed me a wirenut.
The incoming power was just spliced right there wide open and something
in the drawer snagged the neutral and pulled it loose. I lived in an
apartment about that same time that had that type of range. It seemed to
work OK, though I really couldn't say it was any better than a regular
type cooktop. Granted my experience with electric was limited (as it
still is) so it wasn't much of a comparison. Larry
Looking at the product brochures at http://www.aubethermostats.com /,
they're switching thermostats, too, just w/ models as fast as 15-20
second cycle times and solid-state switching instead of mechanical
relays. They don't actually "modulate" output except in the sense of
averaging, same as the range controls.
To do otherwise would require a mechanism to waste the "extra" power
as a in a voltage-divider-type rheostat which would be quite
inefficient and require quite large power resistors or other sinks.
The mass of the burner element is made relatively large in electric
stoves to make the average temperature reasonably constant. Better
stoves control on higher frequency cycles and have better-designed
burners to minimize the thermal cycling -- my Mom used to claim she
could tell the difference between her stove and others in that
regard. Whether real or simply perceived I have no idea... :)
Hmm, good point. Because it uses a triac, I had assumed (incorrectly)
that it works pretty much like a standard household dimmer.
I have the in-floor heat in my den set at 30C and when I started
typing this, my Aube thermostat was showing three wavy bars indicating
the floor was operating at 60 per cent capacity (and what I had
thought to be 540 watts, versus 900 watts). Oddly, the thermostat
will still cycle on and off because I can hear a loud "snap" when it
does this; in fact, it just clicked off seconds ago and I can see
there are now no bars shown on the display. In a few minutes, I
expect to hear it click back on.
I took a look at one of the manuals and it does clearly state the bars
indicate "the percentage of heating time required to maintain the
desired temperature", so that seems to suggest you are correct.
Ah, sure enough, "snap" and we're back to three bars again.
The triac is essentially just a bi-directional gated switching circuit
able to be controlled for either voltage polarity, so unless there is
more internally than that, it is essentially just an enhanced switch.
Less expensive dimmers are essentially the same, more expensive may
include other circuitry to modify the waveform and phase to provide
nearer a sinusoidal voltage, but I'd guess these thermostats don't
have that sophistication.
Thanks. I had only a sketchy understanding of how this technology
works so this helps me considerably. And given these thermostats are
connected to resistance loads that should happily work with pretty
much anything you throw at them, they most likely lack any
sophisticated circuitry, as you suggest.
Which brings me to this question: these thermostats are becomming
increasingly popular and they do work extremely well from a consumer's
point of view, but I wonder what impact they may have on power
quality. I understand triacs can generate some nasty THD numbers; one
thing to dim a 60-watt incandescent bulb but 6,000 watts of electric
heat has to kick things up a notch or two. Any thoughts?
Yeah. There is just a small heater in them that is energized whenever
the stove element is energized, a bimetallic strip thermostat, and a
setting knob. Essentially, you are controlling the temperature inside
the housing of the stove control by setting the knob position. The
heater inside the control operates from zero to 100 percent of the time,
whatever is required to maintain the set temperature. The stove elment
operates off a different contact of the same switch, and this allows you
to continuously vary the average power to the element.
The "infinite heat" stove controls have simple mechanical switches that
are either on or off. They have no effect on power waveform (unlike
On Feb 14, 1:07 am, email@example.com (Dave Martindale) wrote:
That depends on what you mean by "no effect" :) ---
They chop the AC sinusoidal waveform to turn power off and on.
Whether they do it randomly in the cycle or as w/ diac/triac switches
at or very near the crossing voltage makes some difference in what the
resulting waveform is, but in either case the output isn't continuous
and is a chopped sine. The "more expensive" triac dimmers mentioned
earlier have some additional components (usually an RC to introduce a
time delay tied into another diode to bleed the cap while the main
triac isn't conducting to contribute a portion during the "off"
cycle. For incandescent lights, it reduces flicker and "singing"
caused by the harmonics generated in the simple "bang-bang" chopped
For the heater, (and the cooktop range element) the resulting
difference in input waveform would be pretty much immaterial owing to
the higher thermal mass as compared to a bulb filament and the
likelihood of objectionable generated mechanical vibration is much
less again owing to the size/mass.
If, otoh, by no effect you meant "the power waveform is just a
sinusoid with some variable fraction missing" referring to there being
no attempt to compensate, then I agree. Wasn't sure which
interpretation you were intending...
Hopefully, that will help Paul more than confuse further.
First, I was talking about their effect on the current waveform at the
input to the house, or at the output of the utility generator, not the
output to the element.
What I meant was that the waveform may be disturbed for one half-cycle
as the mechanical switch opens or closes at some random time, but then
the switch remains open or closed for many hundreds of cycles before
changing state again. So a fraction of one percent of the waveform
half-cycles are distorted, but the remainder are unmodified sine waves.
To a utility, that's an undistorted waveform.
But a triac dimmer adjusts power by turning on part way through *every*
half cycle, so *every* cycle is distorted. That's what I was comparing
to, and I think what the original poster was referring to.
There's yet another type of modulating control that uses a triac switch
turned on at zero-crossing of the waveform. It can be cycled on or off
quite rapidly to control power - it can let through a few cycles of AC,
then turn off for a few more. So its cycling rate is somewhere between
that of a conventional triac dimmer and a conventional mechanical
"infinite heat" control. I don't know if these are used in any stoves,
but they are used in industrial furnaces. These don't distort the AC
waveform at all.
That's at least theoretically true -- to what extent it is a real
problem I don't know -- it's not quite as bad as a chopped DC in terms
of the generated harmonics and not as much of a problem from high
frequency as a switching power supply owing to the base 60 Hz
frequency, but I don't have any real information at hand on what sort
of problems one might cause in the practical sense.
As I noted in another response, the noticeable effect w/ dimmers is
owing to the small inertia of the filament so that flicker can be
visible and "singing" may sometimes be heard. That's not nearly as
likely w/ the heaters so unless there's something nearby that is
susceptible to the radiated harmonics (AM radio is one likely
candidate, perhaps), it shouldn't cause too much problem. Large
heaters like you're talking about tend to be on dedicated circuits so
there isn't as much likelihood of direct contamination of some
sensitive input supply.
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