"Variable heat" electric range available anywhere?

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 about.
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 ignore it.
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.
Dave
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On Wed, 14 Feb 2007 05:30:27 +0000 (UTC), snipped-for-privacy@cs.ubc.ca (Dave Martindale) wrote:

What I was trying to say before, is that I'd expect the vast majority of overloads to be momentary.

--
Mark Lloyd
http://notstupid.laughingsquid.com
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snipped-for-privacy@cs.ubc.ca (Dave Martindale) writes:

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.
Dave
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Hi Mark,
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 "supper-waiting-on-the-table-when-we-get-home-from-work" type.
And, hey, don't forget. I owe you one!
Cheers, Paul
On Tue, 13 Feb 2007 12:55:47 -0600, Mark Lloyd

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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.
Recognize nonsense?
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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 100000 ovens.
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.
Dave
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Hi Dave,
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 reduced.
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 area.
Please let me know if I'm a little more successful this time out, or if I should be hiding my face. :-0
Cheers, Paul
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wrote:

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?
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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 unlikely.
Dave
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On Mon, 12 Feb 2007 19:23:02 +0000 (UTC), snipped-for-privacy@cs.ubc.ca (Dave Martindale) wrote:

How can that be? Any distortion by the triac appears beyond the triac.
The electricity is billed by what goes through the meter, where it is undistorted.
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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.
Dave
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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
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wrote:

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... :)
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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.
Source: http://www.aubetech.com/manuel/2/TH108PLUS.pdf
Ah, sure enough, "snap" and we're back to three bars again.
Cheers, Paul

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wrote:

...
...
...
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.
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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?
Cheers, Paul

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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 triac dimmers).
Dave
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On Feb 14, 1:07 am, snipped-for-privacy@cs.ubc.ca (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 control case.
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.
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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.
Dave
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wrote:

...
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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