That's a very common statistics mistake. That gives you the probability that all stoves are on at a particular time. What matters is if all stoves are on at ANY time. There's a really big difference there (as big as the difference between a millimeter and the width of the galaxy).
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?
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
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?
When I was a kid (1960's), our old Frigidaire did this. Today (still a kid only bigger), our new Thermador does this. (ours is dual fuel, not because all gas wasn't available, but because we wanted the advantages of dual fuel.)
Our Thermador uses the upper for broiling (duh!), both the upper and lower to preheat, switching to lower only to maintain temperature. The convection setting has its own element.
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.
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
Hi Mike,
That's interesting. I wonder if your Thermador being dual fuel works a little differently from your standard, run of the mill electric range. We have a dual fuel Heartland Legacy, but the original range (another Frigidaire) was all electric and the circuit supplying it is equipped with a 40-amp breaker which, for the moment, I'll assume is the norm. If we abide by the 80 per cent rule and assuming a full 240 volts, that gives us roughly 7,700 watts to work with.
A standard 30-inch range would have four cook-top burners and two oven elements (bake and broil). I guess the question we must ask ourselves is do we have enough capacity at 40-amps to supply all or a reasonable combination of these elements without tripping the breaker? I realize it's not likely we'd have all four burners turned on high and the oven pre-heating, but it would be interesting to see just how far we might push our luck.
Quoting from the Whirlpool's website, "Electric coil ranges usually have two high-output elements (8-inch coils rated 2,600 Watts) and two low-output elements (6-inch coils rated 1,500 Watts)." Using these numbers, if all four burners were turned on high, our combined load would be 8,200-watts (34 amps) or just slightly over 85 per cent of our circuit's capacity.
Now I'm guessing a standard bake element is 3,000-watts and a broil element is about the same or perhaps a little higher. If we assume the two elements total 6,000-watts, we stand at 25 amps or just a little over 60 per cent of total capacity.
If we have our two large burners turned on and both oven elements operating, demand exceeds 11,000-watts (47 amps) and our breaker trips. However, these same two burners and just the bake element drops us back down to 8,200 watts/34 amps which should keep the power flowing.
So, realistically speaking, operating both oven elements on a 40-amp circuit doesn't seem feasible. With dual fuel, it won't be a problem but with an all electric range, you would have to bump things up to 50 or even 60 amps. Any idea what size breaker is normally used for a standard 30-inch range? I'm guessing 40 only by what I see in my own panel, but perhaps 50 or 60 amps is more common.
Cheers, Paul
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
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
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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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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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.
Thanks for describing this in greater detail. I'm seeing more of these new electronic thermostats used in electrically heated homes and so I was curious what impact, if any, they might have on power quality (those nasty third harmonics et al.). I have three in my own home controlling my in-floor radiant heat and have been quite pleased with their performance.
Cheers, Paul
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
The "third harmonic" thing is the result of chopping a DC supply, and not the same as a chopped AC supply. I'm sure there is some 3rd- harmonic content, but with a chopped sine the theoretical waveform won't be the "all odd harmonics in 1/N magnitude" of the chopped DC. OTTOMH I don't recall the characteristics of the transform for the chopped sinusoidal case and was/am too lazy to get up and look for it (and definitely too lazy to work it out :) ), but it's different--just how different was what I was hemming and hawing about. It is, of course, dependent on the phase angle as well as the discontinuity changes characeristics as the chopping point moves through the cycle. Actually, as I think about it, while the zero-switching is advantageous from the standpoint of switching small currents, it is the steepest gradient of voltage change w/ time, so in fact, the worst from the standpoint of generating harmonics. But, the fact that it isn't a square wave means it isn't the odd-harmonics only case.
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
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
My built-in oven (old Frigidaire electric) uses both elements when baking. I found out then the upper element quit working (not a bad element, but the connector). Food would burn on the bottom and still be raw on top.
I'll bet that if you look at the output waveform on an oscilloscope, you'll find that the thermostat is either on or off at any given point in time, and that it cycles between on and off every few seconds in order to modulate the heat. The switching could happen at random times during the AC cycle if a mechanical relay is used, or it might be at zero-crossings if an electronic relay is used.
But a heater has enough thermal inertia that there's no point in switching the current 120 times per second, like a lamp dimmer does, and switching only every few seconds reduces any electrical interference and avoids creating non-sinusoidal current waveforms.
Dave
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